# Laplace asymptotics for generalized K.P.P. equation

ESAIM: Probability and Statistics (2010)

- Volume: 1, page 225-258
- ISSN: 1292-8100

## Access Full Article

top## Abstract

top## How to cite

topRouquès, Jean-Philippe. "Laplace asymptotics for generalized K.P.P. equation." ESAIM: Probability and Statistics 1 (2010): 225-258. <http://eudml.org/doc/197741>.

@article{Rouquès2010,

abstract = {
Consider a one dimensional nonlinear reaction-diffusion equation
(KPP equation) with non-homogeneous second order term, discontinuous
initial condition and small parameter. For points ahead
of the Freidlin-KPP front, the solution tends to 0 and we obtain
sharp asymptotics (i.e. non logarithmic). Our study follows the
work of Ben Arous and Rouault who solved this problem in the
homogeneous case. Our proof is probabilistic, and is based on
the Feynman-Kac formula and the large deviation principle
satisfied by the related diffusions. We use the Laplace method
on Wiener space. The main difficulties come from the nonlinearity
and the possibility for the endpoint of the optimal path to lie
on the boundary of the support of the initial condition.
},

author = {Rouquès, Jean-Philippe},

journal = {ESAIM: Probability and Statistics},

keywords = {Generalized KPP equation / Feynman-Kac formula / diffusion /
large deviations / Laplace method / stochastic Taylor expansion /
Skorokhod integral.; nonlinear diffusion; probabilistic formulation; Feynman-Kac formula},

language = {eng},

month = {3},

pages = {225-258},

publisher = {EDP Sciences},

title = {Laplace asymptotics for generalized K.P.P. equation},

url = {http://eudml.org/doc/197741},

volume = {1},

year = {2010},

}

TY - JOUR

AU - Rouquès, Jean-Philippe

TI - Laplace asymptotics for generalized K.P.P. equation

JO - ESAIM: Probability and Statistics

DA - 2010/3//

PB - EDP Sciences

VL - 1

SP - 225

EP - 258

AB -
Consider a one dimensional nonlinear reaction-diffusion equation
(KPP equation) with non-homogeneous second order term, discontinuous
initial condition and small parameter. For points ahead
of the Freidlin-KPP front, the solution tends to 0 and we obtain
sharp asymptotics (i.e. non logarithmic). Our study follows the
work of Ben Arous and Rouault who solved this problem in the
homogeneous case. Our proof is probabilistic, and is based on
the Feynman-Kac formula and the large deviation principle
satisfied by the related diffusions. We use the Laplace method
on Wiener space. The main difficulties come from the nonlinearity
and the possibility for the endpoint of the optimal path to lie
on the boundary of the support of the initial condition.

LA - eng

KW - Generalized KPP equation / Feynman-Kac formula / diffusion /
large deviations / Laplace method / stochastic Taylor expansion /
Skorokhod integral.; nonlinear diffusion; probabilistic formulation; Feynman-Kac formula

UR - http://eudml.org/doc/197741

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.