Support theorems for degenerate stochastic differential equations with jumps and applications

2018/10/10 by Huijie Qiao, Qiao, Huijie, Jiang-Lun Wu +1
Economics, Econometrics and Finance · Engineering · Mathematics · #60H10 #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1810.04764

openalex publication_date 2018/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper, we are concerned with degenerate stochastic differential equations with jumps. Firstly, we establish two support theorems for the solutions of the degenerate stochastic equations, under different (sufficient) conditions. Secondly, we apply one of our support theorems to a class of degenerate stochastic evolution equations (i.e., infinite-dimensional stochastic differential equations) with jumps to get a characterisation of path-independence for the densities of their Girsanov transformations.

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