A forward-backward stochastic analysis of diffusion flows
Del Moral, Pierre ; Singh, S.S.
HAL, hal-02161914 / Harvested from HAL
Text on HAL
We present forward-backward stochastic semigroup formulae to analyse the difference of diffusion flows driven by different drift and diffusion functions. These formulae are expressed in terms of tangent and Hessian processes and can be interpreted as an extension of the Aleeksev-Gröbner lemma to diffusion flows. We present some natural spectral conditions that allows to derive in a direct way a series of uniform estimates with respect to the time horizon. We illustrate the impact of these results in the context of diffusion perturbation theory, interacting diffusions and discrete time approximations.
Publié le : 2019-06-21
Classification:  Bismut-Elworthy-Li formulae,  Malliavin differential,  Stochastic flows,  variational equations,  tangent and Hessian processes,  perturbation semigroups,  Aleeksev-Gröbner lemma,  Skorohod stochastic integral,  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR],  [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] 
@article{hal-02161914,
     author = {Del Moral, Pierre and Singh, S.S.},
     title = {A forward-backward stochastic analysis of diffusion flows},
     journal = {HAL},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-02161914}
}

Del Moral, Pierre; Singh, S.S. A forward-backward stochastic analysis of diffusion flows. HAL, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/hal-02161914/