Related papers: Wiener integrals, Malliavin calculus and covarianc…

This survey is a preliminary version of a chapter of the forthcoming book "Stochastic Analysis for Poisson Point Processes: Malliavin Calculus, Wiener-It\^o Chaos Expansions and Stochastic Geometry" edited by Giovanni Peccati and Matthias…

We combine Malliavin calculus with Stein's method, in order to derive explicit bounds in the Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a general Gaussian process. We also prove results concerning…

By using Malliavin calculus and multiple Wiener-It\^o integrals, we study the existence and the regularity of stochastic currents defined as Skorohod (divergence) integrals with respect to the Brownian motion and to the fractional Brownian…

We consider Volterra Gaussian processes on [0,T], where T>0 is a fixed time horizon. These are processes of type X_t=\int^t_0 z_X(t,s)dW_s, t\in[0,T], where z_X is a square-integrable kernel, and W is a standard Brownian motion. An example…

We introduce the Wick integral $\int_s^t p(X_u) \Diamond \mathrm{d} X_u$ for a class of stochastic processes $X$ which are not necessarily Gaussian, in the regime of bounded $2> q$-variation. The integral is defined for polynomial…

Malliavin Calculus can be seen as a differential calculus on Wiener spaces. We present the notion of stochastic manifold for which the Malliavin Calculus plays the same role as the classical differential calculus for the differential…

We establish a direct connection between the Feynman-Vernon path integral formalism for open quantum systems and the Wiener path integral used in classical stochastic dynamics. By considering a generalized influence functional in the strong…

We have formulated higher-order integration by parts formulae on the path space restricted between two curves, with respect to pinned/ordinary Wiener measures. The higher-order integration by parts formulae introduce nontrivial boundary…

We provide an overview of some recent techniques involving the Malliavin calculus of variations and the so-called ``Stein's method'' for the Gaussian approximations of probability distributions. Special attention is devoted to establishing…

We investigate Wiener-transformable markets, where the driving process is given by an adapted transformation of a Wiener process. This includes processes with long memory, like fractional Brownian motion and related processes, and, in…

We treat a stochastic integration theory for a class of Hilbert-valued, volatility-modulated, conditionally Gaussian Volterra processes. We apply techniques from Malliavin calculus to define this stochastic integration as a sum of a…

Stochastic processes are considered on free loop spaces, geometric loop and diffeomorphism groups of real and complex manifolds. They are used for investigations of Wiener differentiable quasi-invariant measures on such groups relative to…

We present a multifractal formalism for measures on infinite dimensional metric spaces, in terms of scales instead of dimensions in the classical multifractal analysis. We prove a multifractal formalism with a suitable scaling, called…

Using the Euler--Maruyama technique, we show that a class of Wiener processes exist that are obtained by computing an arbitrary positive power of them. This can be accomplished with a proper set of definitions that makes meaningful the…

We consider a utility maximization problem in a broad class of markets. Apart from traditional semimartingale markets, our class of markets includes processes with long memory, fractional Brownian motion and related processes, and, in…

We introduce a new class of stochastic processes called fractional Wiener-Weierstrass bridges. They arise by applying the convolution from the construction of the classical, fractal Weierstrass functions to an underlying fractional Brownian…

We find an explicit expression for the cross-covariance between stochastic integral processes with respect to a $d$-dimensional fractional Brownian motion (fBm) $B_t$ with Hurst parameter $H>1/2$, where the integrands are vector fields…

For a mixed stochastic differential driven by independent fractional Brownian motions and Wiener processes, the existence and integrability of the Malliavin derivative of its solution are established. It is also proved that the solution…

We consider a mixed stochastic differential equation driven by possibly dependent fractional Brownian motion and Brownian motion. Under mild regularity assumptions on the coefficients, it is proved that the equation has a unique solution.

We study stochastic convolutions providing by fundamental solutions of a class of integrodifferential equations which interpolate the heat and the wave equations. We give sufficient condition for the existence of function--valued…