ROUGH VOLTERRA EQUATIONS 1: THE ALGEBRAIC INTEGRATION SETTING

DOI10.1142/S0219493709002737zbMath1181.60105arXiv0809.2000MaRDI QIDQ3643577

Aurélien Deya, Samy Tindel

Publication date: 9 November 2009

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0809.2000

zbMATH Keywords

fractional Brownian motionstochastic Volterra equations

Mathematics Subject Classification ID

Stochastic integrals (60H05) Stochastic integral equations (60H20)

Related Items (17)

Volterra equations driven by rough signals 2: Higher-order expansions ⋮ Skorohod and Stratonovich integrals for controlled processes ⋮ Stochastic differential equations with nonnegativity constraints driven by fractional Brownian motion ⋮ Existence and smoothness of the density of the solution to fractional stochastic integral Volterra equations ⋮ Perturbed linear rough differential equations ⋮ The extension of step-N signatures ⋮ Rough paths and SPDE ⋮ Ramification of Volterra-type rough paths ⋮ Pathwise regularization of the stochastic heat equation with multiplicative noise through irregular perturbation ⋮ Non-linear rough heat equations ⋮ Paracontrolled distribution approach to stochastic Volterra equations ⋮ Volterra equations driven by rough signals ⋮ Rough Volterra equations. II: Convolutional generalized integrals ⋮ Malliavin calculus for fractional delay equations ⋮ Semilinear fractional stochastic differential equations driven by a γ-Hölder continuous signal with γ > 2/3 ⋮ Time fractional stochastic differential equations driven by pure jump Lévy noise ⋮ STOCHASTIC VOLTERRA EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION WITH HURST PARAMETER H > 1/2

Cites Work

• Curvilinear integrals along enriched paths
• Volterra equations driven by semimartingales
• Large deviations for stochastic Volterra equations
• Stochastic analysis, rough path analysis and fractional Brownian motions.
• Controlling rough paths
• Stochastic Volterra equations with singular kernels
• Anticipating stochastic Volterra equations
• Stochastic Volterra equations with anticipating coefficients
• System Control and Rough Paths

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