2006/07/25 by Abhay G Bhatt, Abhay G. Bhatt, Rajeeva L Karandikar +6
Decision Sciences · Mathematics · #60G17 #60G44 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics #math.PR #msc:60G17 #msc:60G44
paper · pdf · doi:10.48550/arxiv.math/0607613
14 pages
arxiv created 2006/07/25 · openalex publication_date 2006/07/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well-known that well-posedness of a martingale problem in the class of continuous (or r.c.l.l.) solutions enables one to construct the associated transition probability functions. We extend this result to the case when the martingale problem is well-posed in the class of solutions which are continuous in probability. This extension is used to improve on a criterion for a probability measure to be invariant for the semigroup associated with the Markov process. We also give examples of martingale problems that are well-posed in the class of solutions which are continuous in probability but for which no r.c.l.l. solution exists.