Abstract: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} $v$. The analysis focuses on the fact that any Markovian probability measure fulfills an {\it intrinsic martingale problem} for which no uniqueness is required.
From: Francesco Russo [view email] [via CCSD proxy]
[v1]
Thu, 11 Jul 2024 08:38:44 UTC (97 KB)
[v2]
Tue, 13 Jan 2026 10:10:05 UTC (56 KB)
[v3]
Tue, 31 Mar 2026 09:21:14 UTC (58 KB)
[v4]
Fri, 14 Aug 2026 09:31:03 UTC (53 KB)
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