Articlegreen2005

Brownian Representations of Cylindrical Local Martingales, Martingale Problem and Strong Markov Property of Weak Solutions of SPDEs in Banach Spaces

48 citations0/0 files storedCzechoslovak Mathematical Journal

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Stochastic processes and statistical mechanics

Abstract

The paper deals with three issues. First we show a sufficient condition for a cylindrical local martingale to be a stochastic integral with respect to a cylindrical Wiener process. Secondly, we state an infinite dimensional version of the martingale problem of Stroock and Varadhan, and finally we apply the results to show that a weak existence plus uniqueness in law for deterministic initial conditions for an abstract stochastic evolution equation in a Banach space implies the strong Markov property.

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References

2007Brownian Motion and Stochastic Calculus 1988Brownian Motion and Stochastic Calculus 1981Stochastic Integration 1994Introduction to the Theory of Diffusion Processes 2004Uniqueness for stochastic evolution equations in Banach spaces

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2018Stochastic evolution equations in Banach spaces and applications to the Heath–Jarrow–Morton–Musiela equations 2016Cylindrical continuous martingales and stochastic integration in infinite dimensions

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