Absolute continuity of symmetric Markov processes

2004/07/01 by Z. -Q. Chen, Z.-Q. Chen, P. J. Fitzsimmons +5 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Stochastic processes and financial applications #math.PR #msc:31C25 #msc:60J45 #msc:60J57

paper · pdf · doi:10.1214/009117904000000432

published as Annals of Probability 2004, Vol. 32, No. 3A, 2067-2098 · Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000432

openalex publication_date 2004/07/01 · arxiv created 2004/10/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Girsanov’s theorem in the context of symmetric Markov processes, extending earlier work of Fukushima–Takeda and Fitzsimmons on Girsanov transformations of “gradient type.” We investigate the most general Girsanov transformation leading to another symmetric Markov process. This investigation requires an extension of the forward–backward martingale method of Lyons–Zheng, to cover the case of processes with jumps.

Cited by

• Cameron-Martin theorems for sequences of symmetric Cauchy-distributed random variables

Related

• Absolute Continuity of Semimartingales
• Absolute continuity and singularity of probability measures induced by a purely discontinuous Girsanov transform of a stable process
• Markov chain approximations for symmetric jump processes
• A Generalized Backward Equation For One Dimensional Processes
• Characterization of subordinate symmetric Markov processes