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In this paper we study one dimensional backward stochastic differential equations (BSDEs) with random terminal time not necessarily bounded or finite when the generator F ( t , Y , Z
Walsh’s theory of martingale measures in order to deal with stochastic partial differential equations that are second order in time, such as the wave equation and the beam equation,
In the almost last three decades, there have been enormous advances in the study of random field solutions to stochastic partial differential equations (SPDEs) driven by
Stochastic partial differential equations of divergence form with discontinuous and unbounded coefficients are consid- ered in C 1 domains.. Existence and uniqueness results are
We give a new representation of fractional Brownian motion with Hurst parameter H ≤ 1 2 using stochastic partial differential equations.. This representation allows us to use the
In this section, we describe a convenient setting to develop integration by parts methods for Markov operators to reach differential equations on Laplace transforms for.. the
[1] study discretization schemes for stochastic differential equations with multivalued drift coefficients; Martinez and Talay [4] study discretization schemes for diffusion
In the subsequent sections we apply the basic definition to the following partial differential equations and systems: nonlinear Poisson equations, p-Laplace equations,
