Extending the Wong-Zakai theorem to reversible Markov processes
Journal of the European Mathematical Society, Tome 4 (2002) no. 3, pp. 237-269
Cet article a éte moissonné depuis la source EMS Press
We show how to construct a canonical choice of stochastic area for paths of reversible Markov processes satisfying a weak Hölder condition, and hence demonstrate that the sample paths of such processes are rough paths in the sense of Lyons. We further prove that certain polygonal approximations to these paths and their areas converge in p-variation norm. As a corollary of this result and standard properties of rough paths, we are able to provide a significant generalization of the classical result of Wong-Zakai on the approximation of solutions to stochastic differential equations. Our results allow us to construct solutions to differential equations driven by reversible Markov processes of finite p-variation with p4.
@article{JEMS_2002_4_3_a1,
author = {Richard F. Bass and Ben Hambly and Terry J. Lyons},
title = {Extending the {Wong-Zakai} theorem to reversible {Markov} processes},
journal = {Journal of the European Mathematical Society},
pages = {237--269},
year = {2002},
volume = {4},
number = {3},
doi = {10.1007/s100970200040},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s100970200040/}
}
TY - JOUR AU - Richard F. Bass AU - Ben Hambly AU - Terry J. Lyons TI - Extending the Wong-Zakai theorem to reversible Markov processes JO - Journal of the European Mathematical Society PY - 2002 SP - 237 EP - 269 VL - 4 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.1007/s100970200040/ DO - 10.1007/s100970200040 ID - JEMS_2002_4_3_a1 ER -
%0 Journal Article %A Richard F. Bass %A Ben Hambly %A Terry J. Lyons %T Extending the Wong-Zakai theorem to reversible Markov processes %J Journal of the European Mathematical Society %D 2002 %P 237-269 %V 4 %N 3 %U http://geodesic.mathdoc.fr/articles/10.1007/s100970200040/ %R 10.1007/s100970200040 %F JEMS_2002_4_3_a1
Richard F. Bass; Ben Hambly; Terry J. Lyons. Extending the Wong-Zakai theorem to reversible Markov processes. Journal of the European Mathematical Society, Tome 4 (2002) no. 3, pp. 237-269. doi: 10.1007/s100970200040
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