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      Higher order spatial approximations for degenerate parabolic stochastic partial differential equations

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          Abstract

          We consider an implicit finite difference scheme on uniform grids in time and space for the Cauchy problem for a second order parabolic stochastic partial differential equation where the parabolicity condition is allowed to degenerate. Such equations arise in the nonlinear filtering theory of partially observable diffusion processes. We show that the convergence of the spatial approximation can be accelerated to an arbitrarily high order, under suitable regularity assumptions, by applying an extrapolation technique.

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          Author and article information

          Journal
          2012-10-03
          2012-10-04
          10.1137/120893926
          1210.1198

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Custom metadata
          65B05, 60H15, 35K65
          25 pages (minor changes)
          math.NA math.PR

          Numerical & Computational mathematics, Probability

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