Numerical schemes for multivalued backward stochastic differential systems

Lucian Maticiuc; Eduard Rotenstein

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Backward doubly stochastic differential equations with infinite time horizon

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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.

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With the pioneering work of [Pardoux and Peng, (1990) 55–61; Pardoux and Peng, (1992) 200–217]. We have at our disposal stochastic processes which solve the so-called . These processes provide us with a Feynman-Kac representation for the solutions of a class of nonlinear partial differential equations (PDEs) which appear in many applications in the field of Mathematical Finance. Therefore there is a great interest among both practitioners and theoreticians...

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In the present paper, using a Picard type method of approximation, we investigate the global existence of mild solutions for a class of Ito type stochastic differential equations whose coefficients satisfy conditions more general than the Lipschitz and linear growth ones.