Wednesday, July 29, 2026 - 16:30 in V3-201+Zoom
Exponential twist of probability measures: drift correction in term of a generalized gradient
A talk in the Bielefeld Stochastic Afternoon series by
Francesco RUSSO from ENSTA Paris, Institut Polytechnique de Paris
| Abstract: |
This talk will concern the exponential twist, i.e.
a path-integral exponential change of measure,
of a Markovian reference probability measure ${\mathbb P}$.
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 ${\mathbb P}$, 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 $\mathrm{generalized gradient}$ of some
suitable $\mathrm{ value function}$ $v$. Applications of this work
refer to an entropy minimization algorithm.
This work is based on a collaboration with Th. Bourdais (ENSTA and Mazars),
and N. Oudjane (EDF).
Within the CRC this talk is associated to the project(s): A5, B1 |
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