Stochastic switching in infinite dimensions with applications to random parabolic PDE


Journal Article

© 2015 Society for Industrial and Applied Mathematics. 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.

Full Text

Duke Authors

Cited Authors

  • Lawley, SD; Mattingly, JC; Reed, MC

Published Date

  • January 1, 2015

Published In

Volume / Issue

  • 47 / 4

Start / End Page

  • 3035 - 3063

Electronic International Standard Serial Number (EISSN)

  • 1095-7111

International Standard Serial Number (ISSN)

  • 0036-1410

Digital Object Identifier (DOI)

  • 10.1137/140976716

Citation Source

  • Scopus