Non parametric estimation of the diffusion coefficients of a diffusion with jumps

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Schmisser, Emeline¹ 

[1] Univ Lille, CNRS, UMR 8524, Lab Paul Painleve, Lille, France

关键词: Jump diffusions;    Model selection;    Nonparametric estimation;   

DOI  :  10.1016/j.spa.2019.03.003

来源: Elsevier

【 摘 要 】

In this article, we consider a jump diffusion process (X-t)(t >= 0), with drift function b, diffusion coefficient sigma and jump coefficient xi(2). This process is observed at discrete times t = 0, Delta, . . . , n Delta. The sampling interval Delta tends to 0 and the time interval n Delta tends to infinity. We assume that (X-t)(t >= 0) is ergodic, strictly stationary and exponentially beta-mixing. We use a penalized least-square approach to compute adaptive estimators of the functions sigma(2) + xi(2) and sigma(2). We provide bounds for the risks of the two estimators. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free