Fractional backward stochastic differential equations and fractional backward variational inequalities

DOI10.1007/s10959-013-0509-9zbMath1319.60133arXiv1102.3014OpenAlexW3102168844MaRDI QIDQ2346984

Lucian Maticiuc, Tianyang Nie

Publication date: 26 May 2015

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.3014

zbMATH Keywords

fractional Brownian motionMalliavin calculusbackward stochastic differential equationssubdifferential operatorbackward stochastic variational inequalitydivergence-type integral

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Variational inequalities (49J40) Stochastic integrals (60H05) Stochastic calculus of variations and the Malliavin calculus (60H07) Applications of operator theory in probability theory and statistics (47N30)

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Cites Work

• Unnamed Item
• Unnamed Item
• Stochastic calculus with anticipating integrands
• Stochastic analysis of the fractional Brownian motion
• Solving forward-backward stochastic differential equations explicitly -- a four step scheme
• Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than 1/2
• Martingale transforms and Girsanov theorem for long-memory Gaussian processes
• A stochastic maximum principle for processes driven by fractional Brownian motion.
• Backward stochastic differential equations with subdifferential operator and related variational inequalities
• Stochastic differential equations, backward SDEs, partial differential equations
• Stochastic calculus for fractional Brownian motion and related processes.
• Explicit solutions of a class of linear fractional BSDEs
• An inequality of the Hölder type, connected with Stieltjes integration
• Integral transformations and anticipative calculus for fractional Brownian motions
• FRACTIONAL WHITE NOISE CALCULUS AND APPLICATIONS TO FINANCE
• The Malliavin Calculus and Related Topics
• Backward Stochastic Differential Equation Driven by Fractional Brownian Motion
• Stochastic integration with respect to the fractional Brownian motion
• Stochastic Calculus for Fractional Brownian Motion I. Theory
• Stochastic Calculus for Fractional Brownian Motion and Applications
• Stochastic calculus with respect to Gaussian processes