Backward stochastic differential equations (BSDEs) have emerged as a pivotal mathematical tool in the analysis of complex systems across finance, physics and engineering. Their formulation, generally ...

SIAM Journal on Numerical Analysis, Vol. 54, No. 2 (2016), pp. 1093-1119 (27 pages) A fully discrete approximation of the semilinear stochastic wave equation driven by multiplicative noise is ...

In this paper, we study the 2D stochastic quasi-geostrophic equation on 𝕋2 for general parameter α ∈ (0, 1) and multiplicative noise. We prove the existence of weak solutions and Markov selections ...

This paper presents a novel and direct approach to solving boundary- and final-value problems, corresponding to barrier options, using forward pathwise deep learning and forward–backward stochastic ...

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