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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
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    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. --

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    Bibliographic Info

    Paper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 2002,59.

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    Date of creation: 2002
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    Handle: RePEc:zbw:sfb373:200259

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    Keywords: recurrence relation; stochastic recurrence relation; SDDE; SFDE; stochastic delay equations; numerical algorithms; stability; stability regions;

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