| Abstract: |
| We develop a generic scheme to simulate the 2-tuple adapted strong solution in a classical sense to a generalized Cauchy (or called terminal-value) problem, i.e., to a unified system of backward stochastic partial differential equations driven by Brownian motions. The scheme is a completely discrete and iterative algorithm in terms of both time and space, and more importantly, its mean-square convergence with supporting numerical examples is established. In doing so, the system is assumed to be high-dimensional and vector-valued, whose drift and diffusion coefficients may involve nonlinear and high-order partial differential operators. Under general local Lipschitz and linear growth conditions, the unique existence of the 2-tuple adapted strong solution to the system is proved by constructing a suitable Banach space to handle the difficulty that the partial differential orders on both sides of these equations are different. Extensions to the case with Levy jumps and applications in stochastic differential games will also be addressed. |
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