HIGH-DIMENSIONAL LIMITS OF EIGENVALUE DISTRIBUTIONS FOR GENERAL WISHART PROCESS

• 成果类型: Article
• 署名作者: Song, Jian; Yao, Jianfeng; Yuan, Wangjun
• 署名单位: Shandong University; University of Hong Kong; University of Hong Kong
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1539
• 发表日期: 2020
• 页码: 1642-1668
• 关键词: stochastic volatility; laguerre process; MODEL; particles

摘要

In this article, we obtain an equation for the high-dimensional limit measure of eigenvalues of generalized Wishart processes, and the results are extended to random particle systems that generalize SDEs of eigenvalues. We also introduce a new set of conditions on the coefficient matrices for the existence and uniqueness of a strong solution for the SDEs of eigenvalues. The equation of the limit measure is further discussed assuming self-similarity on the eigenvalues.