Displaying similar documents to “A general analytical result for non-linear SPDE's and applications.”

On mild solutions of gradient systems in Hilbert spaces

Andrzej Rozkosz (2013)

Open Mathematics

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We consider the Cauchy problem for an infinite-dimensional Ornstein-Uhlenbeck equation perturbed by gradient of a potential. We prove some results on existence and uniqueness of mild solutions of the problem. We also provide stochastic representation of mild solutions in terms of linear backward stochastic differential equations determined by the Ornstein-Uhlenbeck operator and the potential.

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.

On stochastic differential equations with locally unbounded drift

István Gyöngy, Teresa Martínez (2001)

Czechoslovak Mathematical Journal

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We study the regularizing effect of the noise on differential equations with irregular coefficients. We present existence and uniqueness theorems for stochastic differential equations with locally unbounded drift.

Backward doubly stochastic differential equations with infinite time horizon

Bo Zhu, Baoyan Han (2012)

Applications of Mathematics

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We give a sufficient condition on the coefficients of a class of infinite horizon backward doubly stochastic differential equations (BDSDES), under which the infinite horizon BDSDES have a unique solution for any given square integrable terminal values. We also show continuous dependence theorem and convergence theorem for this kind of equations.