Density estimates for jump diffusion processes
Báo cáo viên: Trần Ngọc Khuê (Phạm Văn Đồng University- Quảng Ngãi)
Thời gian: 14h Thứ 5, ngày 24/06/2021
Địa điểm: P301 nhà A5 hoặc online qua link
Abstract: We consider a real-valued diffusion process with a linear jump term driven by a Poisson point process and we assume that the jump amplitudes have a centered density with finite moments. We show upper and lower estimates for the density of the solution in the case that the jump amplitudes follow a Gaussian or Laplacian law. The proof of the lower bound uses a general expression for the density of the solution in terms of the convolution of the density of the continuous part and the jump amplitude density. The upper bound uses an upper tail estimate in terms of the jump amplitude distribution and techniques of the Malliavin calculus in order to bound the density by the tails of the solution. We also extend the lower bounds to the multidimensional case. Joint work with Arturo Kohatsu-Higa and Eulalia Nualart.

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