On a Cameron--Martin Type Quasi-Invariance Theorem and Applications to Subordinate Brownian Motion

2015/02/21 by Chang‐Song Deng, Chang-Song Deng, Deng, Chang-Song +2
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and financial applications #math.PR

paper · pdf · doi:10.48550/arxiv.1502.06107

arxiv created 2015/02/21 · openalex publication_date 2015/02/21 · arxiv updated 2015/02/24 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We present a Cameron--Martin type quasi-invariance theorem for subordinate Brownian motion. As applications, we establish an integration by parts formula and construct a gradient operator on the path space of subordinate Brownian motion, and we obtain some canonical Dirichlet forms. These findings extend the corresponding classical results for Brownian motion.

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