Open Access
Translator Disclaimer
October 1998 Wavefront propagation for reaction-diffusion systems and backward SDEs
Frédéric Pradeilles
Ann. Probab. 26(4): 1575-1613 (October 1998). DOI: 10.1214/aop/1022855874


We first show a large deviation principle for degenerate diffusion-transmutation processes and study the Riemannian metric associated with the action functional under a Hörmander-type assumption. Then we study the behavior of the solution $u^{\varepsilon}$ of a system of strongly coupled scaled KPP equations. Using backward stochastic differential equations and the theory of Hamilton-Jacobi equations, we show that, when the parabolic operator satisfies a Hörmander-type hypothesis or when the nonlinearity depends on the gradient, the wavefront location is given by the same formula as that in Freidlin and Lee or Barles, Evans and Souganidis. We obtain the exact logarithmic rates of convergence to the unstable equilibrium state in the general case and to the stable equilibrium state when the equations are uniformly positively coupled.


Download Citation

Frédéric Pradeilles. "Wavefront propagation for reaction-diffusion systems and backward SDEs." Ann. Probab. 26 (4) 1575 - 1613, October 1998.


Published: October 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0933.35098
MathSciNet: MR1675043
Digital Object Identifier: 10.1214/aop/1022855874

Primary: 35K57 , 35K65 , 49L25 , 60F10 , 60H30

Keywords: Backward stochastic differential equations , degenerate diffusion-transmutation process , Hamilton-Jacobi equations , large deviations , sub-Riemannian metric , systems of reaction-diffusion equations , viscosity solutions

Rights: Copyright © 1998 Institute of Mathematical Statistics


Vol.26 • No. 4 • October 1998
Back to Top