Backward Itô-Ventzell and stochastic interpolation formulae
Abstract
We present a novel backward Itô-Ventzell formula and an extension of the
Aleeksev-Gr\"obner interpolating formula to stochastic flows. We also present some natural spectral conditions that yield direct and simple proofs of time uniform estimates of the difference between the two stochastic flows when their drift and diffusion functions are not the same, yielding what seems to be the first results of this type for this class of anticipative models.
We illustrate the impact of these results in the context of diffusion perturbation theory, interacting diffusions and discrete time approximations
Keywords
Backward Itô-Ventzell formula
Stochastic flows
Variational equations
Perturbation semigroups
Malliavin differential
Bismut-Elworthy-Li formulae
Skorohod stochastic integral
Tangent and Hessian processes
Aleeksev-Gröbner lemma
variational equations
tangent and Hessian processes
perturba- tion semigroups
backward Itô-Ventzell formula
Bismut-Elworthy-Li formulae Mathematics Subject Classification : 47D07
93E15
60H07
Origin | Files produced by the author(s) |
---|
Loading...