Exponential twist of probability measures: drift correction in term of a generalized gradient
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908922118406144 |
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| author | Bourdais, Thibaut Oudjane, Nadia Russo, Francesco |
| author_facet | Bourdais, Thibaut Oudjane, Nadia Russo, Francesco |
| contents | In this paper we study the exponential twist, i.e. a path-integral exponential change of measure, of a Markovian reference probability measure $¶$. This type of transformation naturally appears in variational representation formulae originating from the theory of large deviations and can be interpreted in some cases, as the solution of a specific stochastic control problem. Under a very general Markovian assumption on $¶$, we fully characterize the exponential twist probability measure as the solution of a martingale problem and prove that it inherits the Markov property of the reference measure. The ''generator'' of the martingale problem shows a drift depending on a {\it generalized gradient} of some suitable {\it value function} $v$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_08291 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exponential twist of probability measures: drift correction in term of a generalized gradient Bourdais, Thibaut Oudjane, Nadia Russo, Francesco Probability In this paper we study the exponential twist, i.e. a path-integral exponential change of measure, of a Markovian reference probability measure $¶$. This type of transformation naturally appears in variational representation formulae originating from the theory of large deviations and can be interpreted in some cases, as the solution of a specific stochastic control problem. Under a very general Markovian assumption on $¶$, we fully characterize the exponential twist probability measure as the solution of a martingale problem and prove that it inherits the Markov property of the reference measure. The ''generator'' of the martingale problem shows a drift depending on a {\it generalized gradient} of some suitable {\it value function} $v$. |
| title | Exponential twist of probability measures: drift correction in term of a generalized gradient |
| topic | Probability |
| url | https://arxiv.org/abs/2407.08291 |