Itô's formula for Gaussian processes with stochastic discontinuities

DOI10.1214/19-AOP1369zbMath1468.60066arXiv1801.09906MaRDI QIDQ2184825

Christian Bender

Publication date: 29 May 2020

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

Full work available at URL: https://arxiv.org/abs/1801.09906

zbMATH Keywords

Gaussian processesstochastic integralsItô's formulastochastic discontinuitiess-transform

Mathematics Subject Classification ID

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

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Jain-Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory
• On Stratonovich and Skorohod stochastic calculus for Gaussian processes
• Tail asymptotics of supremum of certain Gaussian processes over threshold dependent random intervals
• Skorohod integration and stochastic calculus beyond the fractional Brownian scale
• Fractional normal inverse Gaussian diffusion
• Backward SDEs driven by Gaussian processes
• Continuity of Gaussian processes
• Stochastic analysis of the fractional Brownian motion
• Differentiability of six operators on nonsmooth functions and \(p\)-variation. With the collaboration of Jinghua Qian
• An \(S\)-transform approach to integration with respect to a fractional Brownian motion
• Are classes of deterministic integrands for fractional Brownian motion on an interval complete?
• Fractional normal inverse Gaussian process
• Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter \(H \in (0,\frac {1}{2})\)
• An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter.
• Wiener integrals, Malliavin calculus and covariance measure structure
• Chain rules and p-variation
• A generalized white noise space approach to stochastic integration for a class of Gaussian stationary increment processes
• White noise-based stochastic calculus with respect to multifractional Brownian motion
• The Malliavin Calculus and Related Topics
• Wick–Itô formula for regular processes and applications to the Black and Scholes formula
• Gaussian quasimartingales
• Gaussian Hilbert Spaces
• Stochastic Volatility for Lévy Processes
• Wick-Itô Formula for Gaussian Processes
• Fractional Laplace motion
• Stochastic calculus with respect to Gaussian processes
• Stochastic calculus with respect to Gaussian processes