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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Ondrejat, M. Brownian Representations of Cylindrical Local Martingales, Martingale Problem and Strong Markov Property of Weak Solutions of SPDEs in Banach Spaces. Czech Math J 55, 1003–1039 (2005). https://doi.org/10.1007/s10587-005-0084-z
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DOI: https://doi.org/10.1007/s10587-005-0084-z