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Exponential twist of probability measures: Drift correction in term of a generalized gradient

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  • Bourdais, Thibaut
  • Oudjane, Nadia
  • Russo, Francesco

Abstract

In this paper we study the exponential twist, i.e. a path-integral exponential change of measure, of a Markovian reference probability measure P. 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 P, 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 generalized gradient of some suitable value function v. The analysis focuses on the fact that any Markovian probability fulfills an intrinsic martingale problem for which no uniqueness is required.

Suggested Citation

  • Bourdais, Thibaut & Oudjane, Nadia & Russo, Francesco, 2026. "Exponential twist of probability measures: Drift correction in term of a generalized gradient," Stochastic Processes and their Applications, Elsevier, vol. 201(C).
    • Handle: RePEc:eee:spapps:v:201:y:2026:i:c:s0304414926001961
    DOI: 10.1016/j.spa.2026.105064
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