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

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  • Gilsing, Hagen

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.

Suggested Citation

  • Gilsing, Hagen, 2003. "On L2-stability of solutions of linear stochastic delay differential equations," SFB 373 Discussion Papers 2003,51, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:200351
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