White noise-based stochastic calculus with respect to multifractional Brownian motion

DOI10.1080/17442508.2012.758727zbMath1326.60079OpenAlexW1977698657MaRDI QIDQ2875258

Jacques Lévy-Véhel, Joachim Lebovits

Publication date: 14 August 2014

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://hal.inria.fr/inria-00580196/file/StochasticCalculusmBmWhiteNoise_preprint_le_26_03_2011.pdf

zbMATH Keywords

Gaussian processesstochastic calculusmultifractional Brownian motionTanaka formulaItō formula\(S\)-transformwhite noise theoryWick-Itō stochastic integral

Mathematics Subject Classification ID

Gaussian processes (60G15) Fractional processes, including fractional Brownian motion (60G22) White noise theory (60H40) Diffusion processes and stochastic analysis on manifolds (58J65) Stochastic integrals (60H05)

Related Items (16)

A New Approach to Stochastic Integration with Respect to Fractional Brownian Motion for No Adapted Processes ⋮ Girsanov theorem for multifractional Brownian processes ⋮ Differential equations driven by variable order Hölder noise and the regularizing effect of delay ⋮ Itô's formula for Gaussian processes with stochastic discontinuities ⋮ Multifractional Hermite processes: definition and first properties ⋮ On the Tanaka formula for the derivative of self-intersection local time of fractional Brownian motion ⋮ Local times for multifractional Brownian motion in higher dimensions: A white noise approach ⋮ The density of solutions to multifractional stochastic Volterra integro-differential equations ⋮ General transfer formula for stochastic integral with respect to multifractional Brownian motion ⋮ Stochastic integration with respect to multifractional Brownian motion via tangent fractional Brownian motions ⋮ Partial functional quantization and generalized bridges ⋮ Self-intersection local times for multifractional Brownian motion in higher dimensions: A white noise approach ⋮ Stochastic calculus with respect to Gaussian processes ⋮ Mittag-Leffler analysis. II: Application to the fractional heat equation. ⋮ Self-exciting multifractional processes ⋮ An optimal control problem for a linear SPDE driven by a multiplicative multifractional Brownian motion

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