The abstract Riemannian path space.
The fBm Itô's formula through analytic continuation.
The partial Malliavin calculus
The realization of positive random variables via absolutely continuous transformations of measure on Wiener space.
Time reversal for drifted fractional Brownian motion with Hurst index .
Transportation inequalities for stochastic differential equations of pure jumps
For stochastic differential equations of pure jumps, though the Poincaré inequality does not hold in general, we show that W1H transportation inequalities hold for its invariant probability measure and for its process-level law on right continuous paths space in the L1-metric or in uniform metrics, under the dissipative condition. Several applications to concentration inequalities are given.
Trees and asymptotic expansions for fractional stochastic differential equations
In this article, we consider an n-dimensional stochastic differential equation driven by a fractional brownian motion with Hurst parameter H>1/3. We derive an expansion for E[f(Xt)] in terms of t, where X denotes the solution to the SDE and f:ℝn→ℝ is a regular function. Comparing to F. Baudoin and L. Coutin, Stochastic Process. Appl.117 (2007) 550–574, where the same problem is studied, we provide an improvement in three different directions: we are able to consider equations with drift,...