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The stability of stochastic partial differential equations and applications. Theorems on supports

Part of the Lecture Notes in Mathematics book series (LNM,volume 1390)

Abstract

In this paper we present a general result on the stability of stochastic evolution equations and of stochastic partial differential equations with respect to the simultaneous perturbations of the driving semimartingales and of the unbounded operators in the equations, in the topology of uniform convergence on finite time intervals in probability. Hence we obtain theorems on supports for stochastic evolution equations and stochastic partial differential equations. These results are generalizations of the Stroock-Varadhan support theorem of diffusion processes. As applications, we prove theorems on supports for the nonlinear filter in the filtering theory of diffusion processes.

Key words

  • Stochastic partial differential equations
  • semimartingales
  • support of probability measures
  • nonlinear filtering

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© 1989 Springer-Verlag

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Gyöngy, I. (1989). The stability of stochastic partial differential equations and applications. Theorems on supports. In: Da Prato, G., Tubaro, L. (eds) Stochastic Partial Differential Equations and Applications II. Lecture Notes in Mathematics, vol 1390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083939

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  • DOI: https://doi.org/10.1007/BFb0083939

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51510-4

  • Online ISBN: 978-3-540-48200-0

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