On a class of backward doubly stochastic differential equations |
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Authors: | Svetlana Jankovi? Jasmina Djordjevi?Miljana Jovanovi? |
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Affiliation: | Faculty of Science and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia |
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Abstract: | In this paper, a new class of backward doubly stochastic differential equations is studied. This type of equations has a more general form of the forward Itô integrals compared to the ones which have been studied until now. We conclude that unique solutions of these equations can be represented with the help of solutions of the corresponding backward doubly stochastic differential equations, considered earlier in paper [5] by Pardoux and Peng. Some comparison theorems are also given, as well as a probabilistic interpretation for solutions of the corresponding quasilinear stochastic partial differential equations. |
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Keywords: | Backward doubly stochastic differential equations Existence Uniqueness Moment estimates Connections with SPDEs |
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