Brownian representations of cylindrical local martingales, martingale problem and strong Markov property of weak solutions of SPDEs in Banach spaces

Martin Ondreját

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 4, page 1003-1039
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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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 55.4 (2005): 1003-1039. <http://eudml.org/doc/31007>.

@article{Ondreját2005,
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.},
author = {Ondreját, Martin},
journal = {Czechoslovak Mathematical Journal},
keywords = {Brownian representations; martingale problem; strong Markov property},
language = {eng},
number = {4},
pages = {1003-1039},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Brownian representations of cylindrical local martingales, martingale problem and strong Markov property of weak solutions of SPDEs in Banach spaces},
url = {http://eudml.org/doc/31007},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Ondreját, Martin
TI - Brownian representations of cylindrical local martingales, martingale problem and strong Markov property of weak solutions of SPDEs in Banach spaces
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 4
SP - 1003
EP - 1039
AB - 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.
LA - eng
KW - Brownian representations; martingale problem; strong Markov property
UR - http://eudml.org/doc/31007
ER -

References

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  14. 10.4064/dm426-0-1, Dissertationes Mathematicae 426 (2004), 1–63. (2004) MR2067962DOI10.4064/dm426-0-1
  15. 10.1007/BF00534964, Z. Wahrscheinlichkeitstheorie verw. Gebiete 33 (1975), 195–208. (1975) Zbl0304.60032MR0394862DOI10.1007/BF00534964
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