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

In recent papers, McLeish and others have obtained invariance principles for weak convergence of martingales to Brownian motion. We generalize these results to prove that solutions of discrete-time ...

This is a preview. Log in through your library . Abstract We consider the stochastic sequence {Yt}t∈ N defined recursively by the linear relation Yt+1=AtYt+Bt in a random environment. The environment ...

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 ...