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      Stochastic switching in infinite dimensions with applications to random parabolic PDEs

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          Abstract

          We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution. Applying these general results to the heat equation with randomly switching boundary conditions, we find explicit formulae for various statistics of the solution and obtain almost sure results about its regularity and structure. These results are of particular interest for biological applications as well as for their significant departure from behavior seen in PDEs forced by disparate Gaussian noise. Our general results also have applications to other types of stochastic hybrid systems, such as ODEs with randomly switching right-hand sides.

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          Author and article information

          Journal
          2014-07-08
          10.1137/140976716
          1407.2264

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

          Custom metadata
          35R60, 37H99, 46N20, 60H15, 92C30
          27 pages
          math.PR math.DS

          Differential equations & Dynamical systems, Probability

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