Geodesic
Brownian representations of cylindrical local martingales, martingale problem and strong Markov property of weak solutions of SPDEs in Banach spaces
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 4, pp. 1003-1039
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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.
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.
Classification : 60G44, 60H05, 60H15
Keywords: Brownian representations; martingale problem; strong Markov property 
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Ondreját, Martin. Brownian representations of cylindrical local martingales, martingale problem and strong Markov property of weak solutions of SPDEs in Banach spaces. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 4, pp. 1003-1039. http://geodesic.mathdoc.fr/item/CMJ_2005_55_4_a16/

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