A Feynman–Kac formula approach for computing expectations and threshold crossing probabilities of non-smooth stochastic dynamical systems

摘要

We present a computational alternative to probabilistic simulations fornon-smooth stochastic dynamical systems that are prevalent in engineeringmechanics. As examples, we target (1) stochastic elasto-plasticity, whichinvolve transitions between elastic and plastic states, and (2) obstacleproblems with noise, which involve discrete impulses due to collisions with anobstacle. We focus on solving Backward Kolmogorov Equations (BKEs) ofstochastic variational inequalities modelling elasto-plastic and obstacleoscillators. The main challenge in solving BKEs corresponding to these problemsis to deal with the non-standard boundary conditions which describe thebehavior of the underlying process on the boundary. Applications that couldmake use of this framework abound in many areas of science and technology.