Probability Theory and Related Fields

, Volume 116, Issue 3, pp 421–443

Nonlinear stochastic wave and heat equations


  • Szymon Peszat
    • Institute of Mathematics, Polish Academy of Sciences, Św. Tomasza 30/7, 31-027 Kraków, Poland. e-mail:
  • Jerzy Zabczyk
    • Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland. e-mail:

DOI: 10.1007/s004400050257

Cite this article as:
Peszat, S. & Zabczyk, J. Probab Theory Relat Fields (2000) 116: 421. doi:10.1007/s004400050257


We study nonlinear wave and heat equations on ℝd driven by a spatially homogeneous Wiener process. For the wave equation we consider the cases of d = 1, 2, 3. The heat equation is considered on an arbitrary ℝd-space. We give necessary and sufficient conditions for the existence of a function-valued solution in terms of the covariance kernel of the noise.

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© Springer-Verlag Berlin Heidelberg 2000