Stochastic integration with respect to the sub-fractional Brownian motion with

DOI10.1016/j.spl.2011.10.002zbMath1239.60041OpenAlexW2075002336MaRDI QIDQ419214

Chao Chen, Guang Jun Shen

Publication date: 18 May 2012

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2011.10.002

zbMATH Keywords

Malliavin calculusstochastic integrationItô formulaTanaka formulasub-fractional Brownian motion

Mathematics Subject Classification ID

Gaussian processes (60G15) Stochastic integrals (60H05) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (15)

An approximate approach to fuzzy stochastic differential equations under sub-fractional Brownian motion ⋮ On the convergence to the multiple subfractional Wiener-Itō integral ⋮ The structure of autocovariance matrix of discrete time subfractional Brownian motion ⋮ The \(\mathcal S\)-transform of sub-fBm and an application to a class of linear subfractional BSDEs ⋮ Impulsive fractional stochastic differential inclusions driven by sub-Fractional Brownian motion with infinite delay and sectorial operators ⋮ Stochastic Integral for Non-Adapted Processes Related to Sub-Fractional Brownian Motion when $H>1/2$ ⋮ Estimators for the Drift of Subfractional Brownian Motion ⋮ An Approximation of Subfractional Brownian Motion ⋮ Least squares estimator for \(\alpha\)-sub-fractional bridges ⋮ Spectral Theory for Gaussian Processes: Reproducing Kernels, Boundaries, and L²-Wavelet Generators with Fractional Scales ⋮ A universal envelope for Gaussian processes and their kernels ⋮ Stochastic delay evolution equations driven by sub-fractional Brownian motion ⋮ Variations and estimators for self-similarity parameter of sub-fractional Brownian motion via Malliavin calculus ⋮ Approximation of stochastic differential equations driven by subfractional Brownian motion at discrete time observation ⋮ Impulsive stochastic differential equations involving Hilfer fractional derivatives

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Remarks on sub-fractional Bessel processes
• Remarks on asymptotic behavior of weighted quadratic variation of subfractional Brownian motion
• Remarks on an integral functional driven by sub-fractional Brownian motion
• Fractional Brownian density process and its self-intersection local time of order \(k\)
• A series expansion of fractional Brownian motion
• Inner product spaces of integrands associated to subfractional Brownian motion
• Stochastic calculus with anticipating integrands
• Sub-fractional Brownian motion and its relation to occupation times
• Tanaka formula for the fractional Brownian motion.
• On the collision local time of sub-fractional Brownian motions
• Some extensions of fractional Brownian motion and sub-fractional Brownian motion related to particle systems
• Stochastic calculus for fractional Brownian motion and related processes.
• On the Wiener integral with respect to a sub-fractional Brownian motion on an interval
• Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter \(H \in (0,\frac {1}{2})\)
• Limit theorems for occupation time fluctuations of branching systems. I: long-range dependence
• An inequality of the Hölder type, connected with Stieltjes integration
• Integral transformations and anticipative calculus for fractional Brownian motions
• The Malliavin Calculus and Related Topics
• Some properties of the sub-fractional Brownian motion
• Stochastic Calculus for Fractional Brownian Motion and Applications
• Stochastic integral
• Stochastic calculus with respect to Gaussian processes

This page was built for publication: Stochastic integration with respect to the sub-fractional Brownian motion with