On lp-stability of numerical schemes for affine stochastic delay differential equations stochastic recurrance relations

Numerical solutions of SDDE often reflect to only a limited extent the exact solution behaviour. Hence it is necessary to identify those parameters of SDDE and algorithm for which a numerical method in use is reliable. For affine SDDE test equations, there exist estimates of the stability regions of a numerical method. However, these results rely on bounds for covariance terms. In this paper exact hut high dimensional stochastic affine (linear) recurrence relations are derived for some p > 1. A reduction method presented here allows the representation of the corresponding characteristic polynomial as a determinant of a matrix of polynomial coefficients and lower dimension. This can be used to compute non-zero coefficients of the characteristic polynomial for application to stability questions concerning SDDE. A number of areas where work is continuing is indicated.