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Mimicking the marginal distributions of a semimartingale

Abstract : We exhibit conditions under which the flow of marginal distributions of a discontinuous semimartingale $\xi$ can be matched by a Markov process, whose infinitesimal generator is expressed in terms of the local characteristics of $\xi$. Our construction applies to a large class of semimartingales, including smooth functions of a Markov process. We use this result to derive a partial integro-differential equation for the one-dimensional distributions of a semimartingale, extending the Kolmogorov forward equation to a non-Markovian setting.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-00425345
Contributor : Rama Cont <>
Submitted on : Monday, May 23, 2011 - 12:21:56 AM
Last modification on : Wednesday, December 9, 2020 - 3:07:33 PM
Long-term archiving on: : Wednesday, August 24, 2011 - 2:22:28 AM

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  • HAL Id : hal-00425345, version 3
  • ARXIV : 0910.3992

Citation

Amel Bentata, Rama Cont. Mimicking the marginal distributions of a semimartingale. 2009. ⟨hal-00425345v3⟩

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