Displaying similar documents to “An extension of the Yamada-Watanabe condition for pathwise uniqueness to stochastic differential equations with jumps.”

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.

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.

Nonnegative solutions of a class of second order nonlinear differential equations

S. Staněk (1992)

Annales Polonici Mathematici

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A differential equation of the form (q(t)k(u)u')' = λf(t)h(u)u' depending on the positive parameter λ is considered and nonnegative solutions u such that u(0) = 0, u(t) > 0 for t > 0 are studied. Some theorems about the existence, uniqueness and boundedness of solutions are given.