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(Working Paper) Using a purely probabilistic argument, we prove the global well-posedness of multidimensional superquadratic backward stochastic differential equations (BSDEs) without Markovian assumption. The key technique is the interplay…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
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A complex notion of backward stochastic differential equation (BSDE) is proposed in this paper to give a probabilistic interpretation for linear first order complex partial differential equation (PDE). By the uniqueness and existence of…
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Partial differential equations (PDEs) with inputs that depend on infinitely many parameters pose serious theoretical and computational challenges. Sophisticated numerical algorithms that automatically determine which parameters need to be…
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In recent years, there has been a growing interest in leveraging deep learning and neural networks to address scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods…
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