A large-deviation principle for random evolution equations

Mellouk, Mohamed

Bernoulli, Tome 6 (2000) no. 6, p. 977-999 / Harvested from Project Euclid

Résumé

We consider the family of stochastic processes X^ε= {X^ε(t), 0≤t≤1}, ε>0, where X^ε is the solution of the Itô stochastic differential equation

//\rm d}X^ε(t)=\sqrt{ε}σ(X^ε(t),Z(t))\rm d}W_t+b(X^ε(t),Y(t))\rm d}t,//

whose coefficients depend on processes Z(t)= {Z(t),t∈[0,1]} and Y(t)={Y(t),t∈[0,1]}. Using an extended `contraction principle', we give the large-deviation principle (LDP) of X^ε as ε→0. This extends the LDP for a random evolution equation, proved by Yi-Jun Hu, to the case of random diffusion coefficients.

Détail

Publié le : 2000-12-14
Classification:  Hölder spaces,  large-deviation principle,  random evolution equations,  relative compactness