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

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  • Gilsing, Hagen

Abstract

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.

Suggested Citation

  • Gilsing, Hagen, 2002. "On lp-stability of numerical schemes for affine stochastic delay differential equations stochastic recurrance relations," SFB 373 Discussion Papers 2002,59, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:200259
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