A PDE Approach to Certain Large Deviation Problems for Systems of Parabolic Equations

  • L.C. Evans

    Department of Mathematics, University of Maryland, College Park, MD 20742
  • P.E. Souganidis

    Division of Applied Mathematics, Brown University, Providence, RI 02912

Abstract

We prove an exponential decay estimate for solutions of certain scaled systems of parabolic PDE. Our techniques employ purely PDE methods, mainly the theory of viscosity solutions of Hamilton-Jacobi equations, and provide therefore an alternate approach to the probabilistic large deviation methods of Freidlin-Wentzell, Donsker-Varadhan, etc.

Cite this article

L.C. Evans, P.E. Souganidis, A PDE Approach to Certain Large Deviation Problems for Systems of Parabolic Equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989), pp. 229–258

DOI 10.1016/S0294-1449(17)30024-0