Abstract
A gradient operator is defined for the functionals of a non-Markovian jump process Y whose jump times are given by uniform probability laws. The adjoint of this gradient extends the compensated stochastic integral with respect to Y. An explicit representation of the functionals of Y as stochastic integrals is obtained via a Clark formula in two different approaches. The associated Dirichlet forms is studied in order to obtain criteria for the existence and regularity of densities of random variables in infinite dimension.
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Privault, N. Calcul des variations stochastique pour la mesure de densité uniforme. Potential Analysis 7, 577–601 (1997). https://doi.org/10.1023/A:1017974125312
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DOI: https://doi.org/10.1023/A:1017974125312