Geodesic
Extending the Wong-Zakai theorem to reversible Markov processes
Journal of the European Mathematical Society, Tome 4 (2002) no. 3, pp. 237-269.

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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.
DOI : 10.1007/s100970200040
Classification : 60-XX, 00-XX
Keywords: 
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     author = {Richard F. Bass and Ben Hambly and Terry J. Lyons},
     title = {Extending the {Wong-Zakai} theorem to reversible {Markov} processes},
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     publisher = {mathdoc},
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     year = {2002},
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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. http://geodesic.mathdoc.fr/articles/10.1007/s100970200040/

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