Cylindrical Martingale Problems Associated with Lévy Generators

2017/06/19 by Criens, David
#60G48 #60H15 #60J25 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1706.06049

Abstract

We introduce and discuss Lévy-type cylindrical martingale problems on separable reflexive Banach spaces. Our main observations are the following: Cylindrical martingale problems have a one-to-one relation to weak solutions of stochastic partial differential equations. Moreover, well-posed problems possess the strong Markov property and a Cameron-Martin-Girsanov-type formula holds. As applications, we derive existence and uniqueness results.

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