We consider a family of stochastic differential equations with a drift depending on the past history and a delayed diffusion term perturbed by a small parameter epsilon > 0. We establish the asymptotic behaviour as epsilon down arrow 0 for the logarithm of the corresponding family of densities at a fixed time t > 0. The proof needs large deviation estimates and Malliavin calculus.
Stochastic delay equations with hereditarity drift: estimates of the density
FERRANTE, MARCO;
2000
Abstract
We consider a family of stochastic differential equations with a drift depending on the past history and a delayed diffusion term perturbed by a small parameter epsilon > 0. We establish the asymptotic behaviour as epsilon down arrow 0 for the logarithm of the corresponding family of densities at a fixed time t > 0. The proof needs large deviation estimates and Malliavin calculus.File in questo prodotto:
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