2. STOCHASTIC MODELS FOR SYSTEMS OF FORWARD KOLMOGOROV EQUATIONS
Author: YANA BELOPOLSKAYA DOWNLOAD
DOI:
Abstract
Stochastic counterparts of the Cauchy problem for systems of nonlinear second order parabolic equations written in terms of forward SDEs and FBSDEs are derived and studied. There are selected two types of nonlin ear PDE systems arising in applications and there are developed two different stochastic approaches to study them. The stochastic approach to systems of the first type allows to develop a numerical algorithm to construct the Cauchy problem solutions based on the suitable FBSDE and the neural network technique. The stochastic approach to systems of the second type extends the results obtained in the theory of McKean-Vlasov type equations.
Keywords
nonlinear forward Kolmogorov equations and systems, stochastic models, numerical algorithms, neural networks