In this paper we introduce a stochastic integral with respect to the solution X of the fractional heat equation on [0, 1], interpreted as a divergence operator. This allows to use the techniques of the Malliavin calculus in order to establish an Itô-type formula for the process X.

We develop a theory of Malliavin calculus for Banach space valued random variables. Using radonifying operators instead of symmetric tensor products we extend the Wiener-Itô isometry to Banach spaces. In the white noise case we obtain two sided L-estimates for multiple stochastic integrals in arbitrary Banach spaces. It is shown that the Malliavin derivative is bounded on vector-valued Wiener-I...

Via Malliavin calculus, we analyze the limit behavior in distribution of spatial wavelet variation for solution to stochastic linear wave equation with fractional Gaussian noise time and white space. We propose a wavelet-type estimator Hurst parameter this study its asymptotic properties.

Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter H ∈ (0, 1) called the Hurst index. In this note we will survey some facts about the stochastic calculus with respect to fBm using a pathwise approach and the techniques of the Malliavin calculus. Some applications in turbulence and finance will be discussed. Math...

The aim of this work is to study the tail distribution Cox–Ingersoll–Ross (CIR) model driven by fractional Brownian motion. We first prove existence and uniqueness solution. Then based on techniques Malliavin calculus a result established recently in [1], we obtain an explicit estimate for distributions.

This paper surveys some results on Wick product and Wick renormalization. The framework is the abstract Wiener space. Some known results on Wick product and Wick renormalization in the white noise analysis framework are presented for classical random variables. Some conditions are described for random variables whose Wick product or whose renormalization are integrable random variables. Relevan...

Basic derivative formulas are presented for hypoelliptic heat semi-groups and harmonic functions extending earlier work in the elliptic case. Following the approach of 15], emphasis is placed on developing integration by parts formulas at the level of local martingales. Combined with the optional sampling theorem, this turns out to be an eecient way of dealing with boundary conditions, as well ...