MDP for integral functionals of fast and slow processes with averaging

2003/04/27 by Guillin, A., Liptser, R.
#60F10 #60J27 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.math/0304426

Abstract

We establish large deviation principle (LDP) for the family of vector-valued random processes (X^ε,Y^ε),ε→ 0 defined as X^ε_t=(1)/(ε^κ)∫₀^t H(ξ^ε_s,Y^ε_s)ds, dY^ε_t=F(ξ^ε_t,Y^ε_t)dt+ Dε^1/2-κG(ξ^ε_t,Y^ε_t)dW_t, where W_t is Wiener process and ξ^ε_t is fast ergodic diffusion. We show that, under κ

Related

• Examples of moderate deviation principle for diffusion processes
• A large deviation principle for Markovian slow-fast systems
• Moderate deviations principle for systems of slow-fast diffusions
• Equivalences and counterexamples between several definitions of the\n uniform large deviations principle
• Functional large deviations for Stroock's approximation to a class of Gaussian processes with application to small noise diffusions