title: Spectral solution of delayed random walks.
abstract: We develop a spectral method for computing the probability density function for delayed random walks; for such problems, the method is exact to machine precision and faster than existing approaches. In conjunction with a step function approximation and the weak Euler-Maruyama discretization, the spectral method can be applied to nonlinear stochastic delay differential equations (SDDE). In essence, this means approximating the SDDE by a delayed random walk, which is then solved using the spectral method. We carry out tests for a particular nonlinear SDDE that show that this method captures the solution without the need for Monte Carlo sampling.
authors.affiliation: Applied Mathematics Unit, University of California, Merced, 5200 North Lake Road, Merced, California 95343, USA. hbhat@ucmerced.edu
authors.forename: H S
authors.initials: HS
authors.lastname: Bhat
authors.forename: N
authors.initials: N
authors.lastname: Kumar