On L2-stability of solutions of linear stochastic delay differential equations

Hagen Gilsing

No 2003,51, SFB 373 Discussion Papers from Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes

Abstract: Stochastic Delay Differential Equations (SDDE) are Stochastic Functional Differential Equations with important applications. It is of interest to characterize the L2-stability (stability of second moments) of solutions of SDDE. For the class of linear, scalar SDDE we can show that second comoment function of the solution satisfies a partial differential equation (PDE) with time delay and derive a characteristic equation from it determining the asymptotic behaviour of the second moments. Additionally we derive a necessary criterion for weak stationarity of solutions of linear SDDE.

Keywords: SDDE; SFDE; stochastic delay equations; stability; characteristic equation (search for similar items in EconPapers)
Date: 2003
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