Weak symmetric integrals with respect to the fractional Brownian motion

DOI10.1214/17-AOP1227zbMath1430.60036arXiv1606.04046MaRDI QIDQ1660633

David Nualart, Giulia Binotto, Ivan Nourdin

Publication date: 16 August 2018

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

Full work available at URL: https://arxiv.org/abs/1606.04046

zbMATH Keywords

fractional Brownian motionMalliavin calculusStratonovich integralsItô formula in law

Mathematics Subject Classification ID

Gaussian processes (60G15) Stochastic calculus of variations and the Malliavin calculus (60H07) Functional limit theorems; invariance principles (60F17) Foundations of stochastic processes (60G05)

Related Items (7)

On backward problems for stochastic fractional reaction equations with standard and fractional Brownian motion ⋮ Strong solutions for jump-type stochastic differential equations with non-Lipschitz coefficients ⋮ Convergence of trapezoid rule to rough integrals ⋮ Rate of convergence for the weighted Hermite variations of the fractional Brownian motion ⋮ Discrete rough paths and limit theorems ⋮ Symmetric stochastic integrals with respect to a class of self-similar Gaussian processes ⋮ Fluctuations for matrix-valued Gaussian processes

Cites Work

• Central limit theorem for a Stratonovich integral with Malliavin calculus
• Weak convergence of the Stratonovich integral with respect to a class of Gaussian processes
• The weak stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6
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• On Simpson's rule and fractional Brownian motion with \(H = 1/10\)
• Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: the critical case \(H=1/4\)
• A change of variable formula for the 2D fractional Brownian motion of Hurst index bigger or equal to 1/4
• A change of variable formula with Itô correction term
• Central limit theorems for multiple stochastic integrals and Malliavin calculus
• \(m\)-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 \(H \in (0,\frac {1}{2})\)
• Normal Approximations with Malliavin Calculus
• The Malliavin Calculus and Related Topics
• Asymptotics of weighted random sums

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