Stochastic differential equations (SDEs) provide a foundational framework for modelling systems subject to randomness, incorporating both continuous fluctuations and abrupt changes. In recent decades ...

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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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 ...