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Variational calculus on Wiener space

Abstract : This work aims at extending the classical variational formulation of the logarithm of the expectation of e −f with respect to the Wiener measure to more general measures. First we give a sufficient criteria for functions to be strongly differentiable over the Cameron-Martin space. Then we extend the variational formulation to the case of the image measure of a diffusion, and we use this example to generalize the variational formulation to a wide set of measures, while reducing the integrability hypothesis over f and obtaining new results concerning stochastic invertibility and existence of strong solutions of stochastic differential equations. Finally, we extend once more this formulation by considering conditional expectations with respect to the same set of measures.
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Submitted on : Tuesday, August 16, 2022 - 3:58:45 PM
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  • HAL Id : tel-03752346, version 1

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Kevin Hartmann. Variational calculus on Wiener space. Functional Analysis [math.FA]. Télécom ParisTech, 2016. English. ⟨NNT : 2016ENST0049⟩. ⟨tel-03752346⟩

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