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The aim of this CIMPA school is to provide a stimulating intellectual environment for researchers from Viet Nam and neighboring countries in Asia to interact. The school is primarily oriented towards PhD students and young researchers working in the area of stochastic partial differential equations, stochastic dynamics, stochastic analysis and their applications. This school is especially targeted at encouraging gender balance in mathematics.
The program of the school is organized over two weeks. It includes 6 minicourses on chosen topics given by the main speakers and working groups sessions. The latter will help channel scientific discussions and exchange of ideas on the open problems and challenges in the areas described above.
Website: http://math.ac.vn/conference/CIMPA2018
Registration
For registration and application from neighboring developing countries to a CIMPA financial support, follow the instruction link https://www.cimpa.info/en/
PROGRAM
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During the CIMPA school we expect all the participants to be actively involved, for that reason we will encourage the participation during the socalled Questions and Problem sessions (Q&P), which means that, for each of the topics of the main lectures, several problems will be posted to be worked on them during the duration of the school. The objective is that each participant has the chance to work in groups to discuss topics which are closer to each participant's research interests.
Detailed Program
Opening Ceremony on Monday 05.03.2018
 Registration time: 8:008:45
 Opening address, welcome speech from the organisors and presentation from CIMPA representative: 8:459:00
 Location: the opening ceremony and all the lectures take place at Lecture Hall in the 2nd floor  building A6, Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet road, Cau Giay district, Hanoi.
1. Week 1
2 .Week 2

Monday (05.03) 
Tuesday (06.03) 
Wednesday (07.03) 
Thursday (08.03) 
Friday 
Weekend (10.0311.03) 
09:0009:45 
Prof. Nualart's 
Prof. Nualart's 
Prof. Nualart's 
Prof. GarridoAtienza's 
Prof. GarridoAtienza's 
Ha Long Bay TOUR 
09:4510:30 
Prof. Nualart's 
Prof. Nualart's 
Q&P 
Prof. GarridoAtienza's 
Prof. GarridoAtienza's 

10:3011:00 
Coffee break 
Coffee break 
Coffee break 
Coffee break 
Coffee break 

11:0011:45 
Prof. Nualart's 
Prof. Nualart's 
Prof. Millet's 
Prof. GarridoAtienza's 
Prof. GarridoAtienza's 

11:4512:15 
Q&P 
Q&P 
Q&P 
Q&P 
Q&P 

12:1514:00 
Lunch 
Lunch 
Lunch 
Lunch 
Lunch 

14:0014:45 
Prof. Millet's 
Prof. Millet's 

Prof. Schmalfuss' 
Prof. Schmalfuss' 

14:4515:30 
Prof. Millet's 
Prof. Millet's 
Hanoi City TOUR 
Prof. Schmalfuss' 
Prof. Schmalfuss' 

15:3016:00 
Coffee break 
Coffee break 
Coffee break 
Coffee break 

16:0016:45 
Prof. Millet's 
Prof. Millet's 
Prof. Schmalfuss' 
Prof. Schmalfuss' 

16:4517:15 
Q&P 
Q&P 
Q&P 
Q&P 

Thursday (15.03) 
Friday (16.03) 
09:0009:25 

Hiroki Sumi 
09:2509:50 

Yuzuru Sato 
09:5010:15 

The Tuan Hoang 
10:1510:45 

Coffee break 
10:4511:10 

MaxOlivier Hongler 
11:1011:35 

Viet Hung Pham 
11:3512:00 

Javed Hussain 
12:0014:00 
WORKSHOP 
Lunch 
14:0014:25 
Michael Scheutzow 
Toru Sera 
14:2514:50 
Björn Schmalfuss 
Guangqu Zheng 
14:5015:15 
The Anh Cung 
Diu Tran 
15:1515:45 
Coffee break 
Coffee break 
15:4516:10 
Hakima Bessaih 
Ngoc Khue Tran 
16:1016:35 
Hoang Long Ngo 
Ghaus ur Rahman 
16:3517:00 
Tat Dat Tran 
Tien Dung Nguyen 
17:0017:25 

CLOSING 
We would like to create a nice atmosphere between all participants, in which discussions could take place at any moment, just having a coffee or after the "official program". We expect to organize a social hour during the evening of the first day, that could consist of an informal dinner, giving the chance of meeting each participant in a more informal way.
HÀ NỘI CITY TOUR
(CIMPAIMHVAST research school on "Recent developments in stochastic dynamics and
stochastic analysis")
Date: Wednesday 7th March 2018
13h00: Bus and tourist guide will pick you up at Institute of Mathematics, 18 Hoang Quoc Viet
17h30: Drop at Lenid de Ho Guom Hotel (38 Hai Ba Trung Street) for those who stay there. Tour finish at the pick up point.
For more detail, please check the file here
We contacted with a tourism company to organize a two day Ha Long Bay tour in the weekend 1011/03. The tour costs you 110 Euro (or 130 USD). Lecturers are invited to join the tour by the organizing committee, who take care of the cost.
Those who stay in Lenid de Ho Guom and would like to join the tour can contact us, we can help you check out the room for one night 10/3 and use this money to bear some cost for the tour.
For more details of the tour, please check the file here.
On Wednesday 14/03 at 19:0022:00, we will organize a school banquet at Hoa Binh hotel, 27 Ly Thuong Kiet street http://hoabinhhotel.com
WORKSHOP
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There will be a miniworkshop organized after the school is finished. The miniworkshop, which is considered to be a separated activity from the school, aims to encourage potential collaborations in the future. It is scheduled on Thursday 15/03 afternoon and Friday 16/03 of the second week.
1. Hakima Besaih  University of Wyoming, Laramie, USA
Title: Mean field limit of interacting filaments for 3D fluids
Abstract: Families of N interacting curves are considered, with long range, mean field type, interaction. They generalize models based on classical interacting point particles to models based on curves. In this new setup, a mean field result is proven, as N goes to infinity. The limit PDE is vector valued and, in the limit, each curve interacts with a mean field solution of the PDE. Some connection to the 3D Euler equation is established.
2. The Anh Cung – University of Education, Hanoi, Vietnam
Title: On the existence and longtime behavior of solutions to stochastic threedimensional NavierStokesVoigt equations
Abstract: We consider the 3D stochastic NavierStokesVoigt equations in bounded domains with homogeneous Dirichlet boundary conditions. First, we prove the existence and uniqueness of solutions to the problem. Then we investigate the mean square exponential stability and the almost sure exponential stability of the stationary solutions.
3. The Tuan Hoang  Institute of Mathematics, VAST, Hanoi, Vietnam
Title: Asymptotic separation between solutions of Caputo fractional stochastic differential equations
Abstract: In this talk, we formulate a generic condition on the coefficient of a stochastic phase oscillator for which the Lyapunov exponent is negative.
Consequently, the generated random dynamical system exhibits a synchronization
4. Ghaus ur Rahman  University of Swat Khyber Pakhtunkhawa, Pakistan.
Title: Dynamical Aspects of Stochastic Childhood Diseases Model
Abstract: In this talk, we look at the dynamics of an epidemic model of the infectious childhood diseases. We take a look at the asymptotic behavior of the stochastic model near the equilibrium points, and additionally study the model when the coefficients of the noise are small. Moreover we show that the model is ergodic.
5. Javed Hussain  Sukkur IBA University, Pakistan
Title: Large deviation principle for stochastic heat equation on Hilbert manifold
Abstract: In this talk our aim is to present Large Deviation property for the solution of stochastic heat equation on Hilbert manifold with stratonovich noise. For this we are going to employ the weak convergence method for studying large deviation principle . (Joint work with Prof. Zdzislaw Brzezniak, University of York).
6. MaxOlivier Hongler  EPFL STI SMTGE, Lausanne Switzerland
Title: Solvable nonlinear reactiondiffusion equations and their connection to optimal control problems.
Abstract: Generalising a connection between nonlinear discrete velocities Boltzmann equation and solvable optimal control problem, we construct a new class of fully solvable nonlinear reactiondiffusion dynamics. In parallel, we show how the cost function of the control problem is naturally related to a large deviations principle.
7. Viet Hung Pham, Institute of Mathematics Hanoi
Title: Persistence probability of random polynomials
Abstract: We study the persistence probability of random polynomials where the polynomials stay positive or equivalently have no real roots. The motivation comes from some applications in statistical physics and evolutionary game theory. Using a method proposed by Dembo and Mukherjee, we can provide the persistence exponents. In joint work with Van Hao Can and Duong Manh Hong.
8. Hoang Long Ngo – University of Education, Hanoi, Vietnam
Title: Geometric numerical integration for some classes of stochastic noncolliding particle systems.
Abstract: We present a semiimplicit EulerMaruyama approximation scheme for some classes of stochastic noncolliding particle systems such as the DysonBrownian motion. We study its rates of convergence in the strong sense and show that the scheme preserves some geometric properties of the systems.
This is a joint work with Dai Taguchi (Osaka University).
9. Tien Dung Nguyen  FPT University, Hanoi, Vietnam
Title: Some sufficient conditions for Novikov's criterion
Authors: Nguyen Tien Dung and Nguyen Van Tan
Abstract: In this talk, we employ the techniques of Malliavin calculus to provide some sufficient conditions for a stochastic process to satisfy Novikov's criterion. In particular, we obtain an improvement for Buckdahn's results established in [1]. References
[1] R. Buckdahn, Anticipative Girsanov transformations. Probab. Theory Rel. Fields 89 (1991) 211238.
[2] N.T. Dung, Some sufficient conditions for Novikov's criterion. To appear in Proceedings of the AMS, 2018.
10. Toru Sera  Kyoto University, Japan
Title: Multiray generalization of the arcsine laws for interval maps
Abstract: We present a distributional limit theorem for the occupation ratio measures of interval maps with indifferent fixed points. This limit theorem is a multiray extension of Thaler's generalized arcsine laws [1], and is also based on studies of occupation times of diffusion processes on multiray. This is a joint work with Kouji Yano (Kyoto University).
[1] M. Thaler, A limit theorem for sojourns near indifferent fixed points of onedimensional maps, Ergodic Theory Dynam. Systems 22 (2002), no. 4, 12891312. MR1926288
11. Yuzuru Sato  Hokkaido University, Japan
Title: Stochastic chaos in a turbulent swirling flow
Abstract: We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can first reconstruct the associated turbulent attractor and then follow its route towards chaos. We further show that the experimental attractor can be modeled by stochastic Duffing equations, that match the quantitative properties of the experimental flow, namely the number of quasistationary states and transition rates among them, the effective dimensions, and the continuity of the first Lyapunov exponents. Such properties can neither be recovered using deterministic models nor using stochastic differential equations based on effective potentials obtained by inverting the probability distributions of the experimental global observables. Our findings open the way to low dimensional modeling of systems featuring a large number of degrees of freedom and multiple quasistationary states.
12. Michael Scheutzow  TU Berlin, Germany
Title: Minimal attractors.
Abstract: It is wellknown that a random attractor of a random dynamical system which attracts all compact sets is unique while this is not true for a random point attractor (which attracts all deterministic points). We show that if a random point attractor exists then there is always a smallest such point attractor (no matter whether the attraction is in the pullback sense or in probability).
We also provide generalizations to other families of attracted sets and provide an example showing that a smallest forward attractor may not exist. This is joint work with Hans Crauel (Frankfurt).
13. Bjoern Schmalfuss  FriedrichSchillerUniversitaet Jena, Germany
Title: Synchronization of a coupled system of stochastic parabolic differential equations.
Abstract: We consider a system of two spde where the linear parts generate an analytic semigroup. The coupling operator is linear and positive. We formulate conditions for the existence of a random attractor for this system. This attractor has a particular shape which can be interpreted as synchronization.
14. Hiroki Sumi  Kyoto University, Japan
Title: Weak mean stability in random holomorphic dynamical systems.
Abstract: We consider random holomorphic dynamical systems generated by holomorphic families of rational maps on the Riemann sphere. We introduce the notion of “weak mean stability” and show several properties of weakly mean stable systems. Also, we show that generic systems are weakly mean stable. For the preprint, see H. Sumi, Negativity of Lyapunov Exponents and Convergence of Generic Random Polynomial Dynamical Systems and Random Relaxed Newton’s Methods, preprint, https://arxiv.org/abs/1608.05230.
15. Thi Thanh Diu Tran  University of Luxembourg, Luxembourg
Title: Statistical inference for Vasicektype model driven by Hermite processes
Abstract: Let {Z_t^{q,H} ,t \ge {\rm{0}}} denote a Hermite process of order q\geq 1 and selfsimilarity parameter H\left( {\frac{{\rm{1}}}{{\rm{2}}},{\rm{1}}} \right) . This process is selfsimilar, has stationary increments and exhibits longrange dependence. When q= 1 it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as q\geq 2 .
In this talk, we deal with the following Vasicektype model driven by Z^{q,H}:
X_{\rm{0}} = {\rm{0,}}dX_t = a\left( {b  X_t } \right)dt + dZ_t^{q,H} ,t \ge {\rm{0}}
where a>0 and b\in R are considered as unknown drift parameters. We provide estimators for a and b based on continuoustime observations. For all possible values of H and q, we prove strong consistency and we analyze the asymptotic fluctuations. Joint work with Ivan Nourdin
16. Tat Dat Tran – MPI MIS, Germany
Title: Free energy functional method and its applications to WrightFisher model
Abstract: In this talk, I will first introduce the most popular model in population genetics, the WrightFisher model, which can be approximated as a diffusion process in a Riemannian manifold with corners. The conditional density function of the process is known as the solution of a forward Kolmogorov equation (also known by physicists as a FokkerPlanck equation). The difficulty is that the generator is singular and the boundary of the domain is not smooth. I will then discuss about a concept from stochastic mechanism socalled free energy functional and how to apply it in this setting. In particular, I shall provide a necessary and sufficient condition in terms of mutation and selection coefficients under which the WrightFisher diffusion process will possess a free energy functional. This then also is a necessary and sufficient condition for the existence of a unique reversible probability density with respect to the Lebesgue measure. Moreover, by using BakryEmery techniques, I will show that under an additional condition, the flow of probability densities exponentially converges to the reversible one in some distance such as total variation. Some open problems will also be discussed.
17. Ngoc Khue Tran  Pham Van Dong University, Quangngai, Vietnam
Title: Local asymptotic properties for the growth rate of a jumptype CIR process.
Abstract: In this talk, we consider a onedimensional jumptype CoxIngersollRoss process driven by a Brownian motion and a subordinator, whose growth rate is a unknown parameter. The Lévy measure of the subordinator is finite or infinite. Considering the process observed continuously or discretely at high frequency, we derive the local asymptotic properties for the growth rate. Three cases are distinguished: subcritical, critical and supercritical. Local asymptotic normality (LAN) is proved in the subcritical case, local asymptotic quadraticity (LAQ) is derived in the critical case, and local asymptotic mixed normality (LAMN) is shown in the supercritical case. Our approach is based on Girsanov's theorem and Malliavin calculus. This is a joint work with Mohamed Ben Alaya, Ahmed Kebaier and Gyula Pap.
18. Guangqu Zheng  University of Luxembourg, EschsurAlzette, Luxembourg
Title: Central limit theorem on Gaussian, Poisson Wiener chaos
Abstract: This talkpresents a new/elementary strategy of proving CLT on Wiener chaos via Stein’s method of exchangeable pairs. We will begin with construction of Gaussian, Poisson Wiener chaos, then introduce the natural exchangeable pair couplings motivated by the classical Mehler formulae. Then a unified proof follows for CLT on Gaussian, Poisson Wiener chaos, together with a transfer principle.
LECTURES
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The proposed lecturers for this school, and suggested topics of their lectures, are the following:
1. Hakima BESSAIH (University of Wyoming Laramie, WY, USA): An introduction to stochastic fluid dynamics.
Abstract: We will give an overview of some models motivated by Hydrodynamics. These models are described by the NavierStokes equations and related models driven by a noise. We will study existence and uniqueness of solutions, the continuous dependence with respect to initial conditions and the longtime behavior of solutions through their invariant measures and/or random attractors. Moreover, we will tackle some results about regularity of solutions. We will mainly deal with the 2D case. The 3D case will be studied thought some approximations like the alpha models. \\
2. María J. GARRIDOATIENZA (University of Sevilla, Spain): Fractional Calculus and Stochastic Differential/Partial Equations driven by fractional noise.
Abstract: The first goal of this course will be to study the existence and uniqueness of equations driven by Hölder continuous functions, for which we will make use of tools of Fractional Calculus. Remarkable differences will appear depending than the Hölder exponent is greater or smaller than 1/2. More precisely, we will pay special attention to the study of pathwise solutions of stochastic equations driven by a fractional Brownian motion, when the Hurst parameter H>1/2 as well as when 1/3<H<1/2, emphasizing the different methods needed to handle both situations. In a second part of the course, and thanks to the fact that the solutions of the equations will generate a cocycle, we will investigate the longtime behaviour of the solutions by analyzing the random attractor associate to these equations.
Annie MILLET (Université Paris 1, France): An introduction to Large Deviations for SDEs and SPDEs.
Abstract: The aim of the course is to give an introduction to usual techniques to prove Large Deviations Principles (LDP) either from scratch (for empirical means, Markov chains and Gaussian processes) or to deduce them from already known LDP results by means of "continuous maps except on an exponentially small set" or the Varadhan Lemma. The course will cover the following 6 topics: 1. The log Laplace transform and its Legendre transform. 2. The Ellis Görtner theorem and applications to Markov chains. 3. Schilder's theorem for Brownian motion and some general Gaussian processes. 4. The contraction principle; the FreidlinWentzell inequality. 5. Varadhan's Lemma and the inverse Bryc Lemma; the weak convergence approach to LDP. 6. Applications to some SPDEs (such as the stochastic 2D Navier Stokes equations).
David NUALART (University of Kansas, USA): Rough Path Analysis.
Abstract: This course is an introduction to the theory of rough paths analysis, which aims to solve multidimensional differential equations controlled by a deterministic input forcing, which has finite pvariaton for some p>1. First we will treat the case p<2, when the equation can be formulated using Young's integral, thus one can establish the existence and uniqueness of a solution to the equation. For the case p between 2 and 3, we will define integrals with respect to rough paths, applying Gubinelli's approach of controlled paths. Using rough paths integrals, we will construct and show the continuity of the socalled Ito Lyons map that defines the solution to the differential equation as a function of the enhanced input signal. As an application we will discuss the classical Ito and Stratonovich SDE driven by a standard Brownian and SDE driven by a fractional Brownian motion.
Björn SCHMALFUSS, (Universität Jena, Germany): Random dynamical systems.
Abstract: The content of these lectures is to consider dynamical systems under the influence of noise. At first we give a description of a general (ergodic) noise. Examples for this kind of noise are the white noise, the OrnsteinUhlenbeck noise, fractional noise and Lévy noise. Considering systems under the influence of noise we have to study instead of a semigroup a socalled cocycle. Under appropriate measurability assumptions a random dynamical system is a cocycle. We will introduce steady states, bifurcations of steady states, stable, unstable, inertial manifolds, and attractors for random dynamical systems. We then will consider several examples from the theory of stochastic random pde's generating random dynamical systems and discuss their dynamical behavior by means of these objects.
Michael SCHEUTZOW (TU Berlin, Germany): Stochastic Delay Equations.
Abstract: Unlike ordinary stochastic differential equations in ddimensional Euclidean space driven by multidimensional Brownian motion, the drift and/or diffusion coefficients of a stochastic delay differential equation (SDDE) do not only depend on the current state but also on the state in the past. Therefore, solutions are not Markov processes when considering in the Euclidean phase space, but typically generate Markov processes taking values on some function space, for example the space of continuous functions on [1,0] in case the maximal delay is 1. We will briefly discuss existence and uniqueness of solutions and then turn to the question of existence and uniqueness of invariant probability measures for the solution Markov process. Methods developed in joint work with Martin Hairer and Jonathan Mattingly and further refined in joint work with Alex Kulik will be discussed.
REGISTRATION
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For others, please fill in the registration form (download http://math.ac.vn/conference/CIMPA2018/) and email it to This email address is being protected from spambots. You need JavaScript enabled to view it.
Registration deadline: November 5, 2017