Nonlinear fractional stochastic PDEs and BDSDEs with Hurst parameter in (1/2,1)

DOI10.1016/j.sysconle.2012.02.011zbMath1250.93115OpenAlexW1982917178MaRDI QIDQ450798

Shuai Jing

Publication date: 14 September 2012

Published in: Systems \& Control Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.sysconle.2012.02.011

zbMATH Keywords

fractional Brownian motionstochastic partial differential equationbackward doubly stochastic differential equationDoss-Sussmann transformationRusso-Vallois integralstochastic viscosity solution

Mathematics Subject Classification ID

Nonlinear systems in control theory (93C10) Transformations (93B17) Stochastic systems in control theory (general) (93E03) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Fractional partial differential equations (35R11)

Related Items (6)

Stability of delayed impulsive stochastic differential equations driven by a fractional Brown motion with time-varying delay ⋮ BSDEs generated by fractional space-time noise and related SPDEs ⋮ Nonlinear Feynman--Kac formulas for Stochastic Partial Differential Equations with Space-Time Noise ⋮ Anticipative backward stochastic differential equations driven by fractional Brownian motion ⋮ Mean-field backward stochastic differential equations driven by fractional Brownian motion ⋮ Forward integration, convergence and non-adapted pointwise multipliers

Cites Work

• Unnamed Item
• Unnamed Item
• Semilinear backward doubly stochastic differential equations and SPDEs driven by fractional Brownian motion with Hurst parameter in \((0,1/2)\)
• Integration with respect to fractal functions and stochastic calculus. I
• Forward, backward and symmetric stochastic integration
• Backward doubly stochastic differential equations and systems of quasilinear SPDEs
• Evolution equations driven by a fractional Brownian motion
• Differential equations driven by fractional Brownian motion
• Backward stochastic differential equations and partial differential equations with quadratic growth.
• Stochastic viscosity solutions for nonlinear stochastic partial differential equations. I
• The generalized covariation process and Itô formula
• Stochastic calculus for fractional Brownian motion and related processes.
• An inequality of the Hölder type, connected with Stieltjes integration
• Integration with respect to Fractal Functions and Stochastic Calculus II
• FRACTIONAL BROWNIAN MOTION AND STOCHASTIC EQUATIONS IN HILBERT SPACES
• Probabilistic interpretation for systems of quasilinear parabolic partial differential equations
• User’s guide to viscosity solutions of second order partial differential equations
• Anticipative Girsanov transformations and Skorohod stochastic differential equations
• Elements of Stochastic Calculus via Regularization
• Stochastic Calculus for Fractional Brownian Motion and Applications

This page was built for publication: Nonlinear fractional stochastic PDEs and BDSDEs with Hurst parameter in (1/2,1)