Displaying similar documents to “An averaging principle for stochastic evolution equations. I.”

Regularity results for infinite dimensional diffusions. A Malliavin calculus approach

Stefano Bonaccorsi, Marco Fuhrman (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We prove some smoothing properties for the transition semigroup associated to a nonlinear stochastic equation in a Hilbert space. The proof introduces some tools from the Malliavin calculus and is based on a integration by parts formula.

Multivalued backward stochastic differential equations with time delayed generators

Bakarime Diomande, Lucian Maticiuc (2014)

Open Mathematics

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Our aim is to study the following new type of multivalued backward stochastic differential equation: - d Y t + ∂ φ Y t d t ∋ F t , Y t , Z t , Y t , Z t d t + Z t d W t , 0 ⩽ t ⩽ T , Y T = ξ , where ∂φ is the subdifferential of a convex function and (Y t, Z t):= (Y(t + θ), Z(t + θ))θ∈[−T,0] represent the past values of the solution over the interval [0, t]. Our results are based on the existence theorem from Delong Imkeller, Ann. Appl. Probab., 2010, concerning backward stochastic differential equations with time delayed generators.