On Stratonovich and Skorohod stochastic calculus for Gaussian processes

DOI10.1214/12-AOP751zbMath1274.60219arXiv1101.3441OpenAlexW2064428637MaRDI QIDQ373592

Yaozhong Hu, Maria Jolis, Samy Tindel

Publication date: 17 October 2013

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.3441

zbMATH Keywords

Gaussian processesMalliavin calculusItô's formularough paths

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic calculus of variations and the Malliavin calculus (60H07) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (12)

Skorohod and Stratonovich integrals for controlled processes ⋮ Berry-Esséen bound for the parameter estimation of fractional Ornstein-Uhlenbeck processes with the hurst parameter H∈(0,12) ⋮ Stratonovich type integration with respect to fractional Brownian motion with Hurst parameter less than \(1/2\) ⋮ Itô's formula for Gaussian processes with stochastic discontinuities ⋮ Parameter estimation for fractional Ornstein-Uhlenbeck processes of general Hurst parameter ⋮ Rough paths and symmetric-Stratonovich integrals driven by singular covariance Gaussian processes ⋮ Feynman-Kac formula for the heat equation driven by fractional noise with Hurst parameter \(H < 1/2\) ⋮ A Stratonovich-Skorohod integral formula for Gaussian rough paths ⋮ On the \(\frac{1}{H}\)-variation of the divergence integral with respect to fractional Brownian motion with Hurst parameter \(H < \frac{1}{2}\) ⋮ Skorohod and rough integration for stochastic differential equations driven by Volterra processes ⋮ Mean-field backward stochastic differential equations driven by fractional Brownian motion ⋮ Least squares estimator of fractional Ornstein-Uhlenbeck processes with periodic mean for general Hurst parameter

Cites Work

• Unnamed Item
• A construction of the rough path above fractional Brownian motion using Volterra's representation
• Limit theorems for nonlinear functionals of Volterra processes via white noise analysis
• On the Wiener integral with respect to the fractional Brownian motion on an interval
• Milstein's type schemes for fractional SDEs
• Hölder-continuous rough paths by Fourier normal ordering
• Wick calculus for nonlinear Gaussian functionals
• Differential equations driven by rough signals
• Stochastic analysis of the fractional Brownian motion
• Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index \(H\geq\frac 1 4\).
• Stochastic integration with respect to Volterra processes
• Stochastic analysis, rough path analysis and fractional Brownian motions.
• Controlling rough paths
• Discretizing the fractional Lévy area
• Rough evolution equations
• An extension theorem to rough paths
• \(m\)-order integrals and generalized Itô's formula; the case of a fractional Brownian motion with any Hurst index
• Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter \(H \in (0,\frac {1}{2})\)
• Integral transformations and anticipative calculus for fractional Brownian motions
• The Malliavin Calculus and Related Topics
• Multidimensional Stochastic Processes as Rough Paths
• System Control and Rough Paths
• Stochastic Calculus for Fractional Brownian Motion I. Theory
• An Introduction to (Stochastic) Calculus with Respect to Fractional Brownian Motion
• Wick-Itô Formula for Gaussian Processes
• Markov Processes, Gaussian Processes, and Local Times
• Stochastic calculus with respect to Gaussian processes

This page was built for publication: On Stratonovich and Skorohod stochastic calculus for Gaussian processes