A parabolic stochastic differential equation with fractional Brownian motion input

DOI10.1016/S0167-7152(98)00147-3zbMath0937.60064OpenAlexW2079254416WikidataQ115339563 ScholiaQ115339563MaRDI QIDQ1304058

V. V. Anh, Wilfried Grecksch

Publication date: 7 June 2000

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-7152(98)00147-3

Mathematics Subject Classification ID

Brownian motion (60J65) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (52)

Variational solutions for partial differential equations driven by a fractional noise ⋮ Sharp mean-square regularity results for SPDEs with fractional noise and optimal convergence rates for the numerical approximations ⋮ Random Dynamical Systems and Stationary Solutions of Differential Equations Driven by the Fractional Brownian Motion ⋮ The continuity, regularity and polynomial stability of mild solutions for stochastic 2D-Stokes equations with unbounded delay driven by tempered fractional Gaussian noise ⋮ Well-posedness of stochastic KdV-BO equation driven by fractional Brownian motion ⋮ Fractional stochastic Volterra equation perturbed by fractional Brownian motion ⋮ Fractional measure-dependent nonlinear second-order stochastic evolution equations with Poisson jumps ⋮ Kolmogorov equation and large-time behaviour for fractional Brownian motion driven linear SDE's. ⋮ On inverse initial value problems for the stochastic strongly damped wave equation ⋮ Young integrals and SPDEs ⋮ Stochastic equations in Hilbert space with a multiplicative fractional Gaussian noise ⋮ Stochastic pseudo-parabolic equations with fractional derivative and fractional Brownian motion ⋮ A NOTE ON VARIATIONAL SOLUTIONS TO SPDE PERTURBED BY GAUSSIAN NOISE IN A GENERAL CLASS ⋮ Abstract functional second-order stochastic evolution equations with applications ⋮ Asymptotic behaviours of a stochastic delay equation driven by an fBm in Hilbert space ⋮ Pathwise solutions of SPDEs driven by Hölder-continuous integrators with exponent larger than \(1/2\) and random dynamical systems ⋮ Stochastic delay differential equations in a Hilbert space driven by fractional Brownian motion ⋮ Cylindrical fractional Brownian motion in Banach spaces ⋮ Local L^p-solution for semilinear heat equation with fractional noise ⋮ Existence and uniqueness of solutions of nonlinear fractional stochastic differential systems with nonlocal functional boundary conditions ⋮ Transport equations with fractal noise-existence, uniqueness and regularity of the solution ⋮ Evolution equations driven by a fractional Brownian motion ⋮ Stochastic elastic equation driven by multiplicative multi-parameter fractional noise ⋮ Retarded evolution systems driven by fractional Brownian motion with Hurst parameter \(H>1/2\) ⋮ Measure-dependent stochastic nonlinear beam equations driven by fractional Brownian motion ⋮ Abstract functional stochastic evolution equations driven by fractional Brownian motion ⋮ An Infinite-Dimensional Fractional Linear Quadratic Regulator Problem ⋮ A FILTERING PROBLEM FOR A LINEAR STOCHASTIC EVOLUTION EQUATION DRIVEN BY A FRACTIONAL BROWNIAN MOTION ⋮ Fractional stochastic partial differential equation for random tangent fields on the sphere ⋮ Stochastic evolution equations with Volterra noise ⋮ Infinite dimensional pathwise Volterra processes driven by Gaussian noise -- probabilistic properties and applications -- ⋮ On a class of measure-dependent stochastic evolution equations driven by fbm ⋮ A class of second-order McKean-Vlasov stochastic evolution equations driven by fractional Brownian motion and Poisson jumps ⋮ The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion ⋮ Weak solutions for stochastic differential equations with additive fractional noise ⋮ Sharp Gaussian regularity on the circle, and applications to the fractional stochastic heat equation ⋮ Stochastic Burgers' equation driven by fractional Brownian motion ⋮ Existence and stability for fractional parabolic integro-partial differential equations with fractional Brownian motion and nonlocal condition ⋮ On Parabolic Volterra Equations Disturbed by Fractional Brownian Motions ⋮ Q-Fractional Brownian Motion in Infinite Dimensions with Application to Fractional Black–Scholes Market ⋮ Solutions of linear and semilinear distributed parameter equations with a fractional Brownian motion ⋮ Stochastic elastic equation driven by fractional Brownian motion ⋮ Regularity of Backward Stochastic Volterra Integral Equations in Hilbert Spaces ⋮ Regularity of the solutions to SPDEs in metric measure spaces ⋮ STOCHASTIC INTEGRATION FOR FRACTIONAL BROWNIAN MOTION IN A HILBERT SPACE ⋮ Gradient type noises. II: Systems of stochastic partial differential equations ⋮ Ergodicity and parameter estimates for Infinite-dimensional fractional Ornstein-Uhlenbeck process ⋮ Approximate controllability of stochastic equations in a Hilbert space with fractional Brownian motions ⋮ Existence and uniqueness of mild solution to fractional stochastic heat equation ⋮ Stochastic Korteweg-de Vries equation driven by fractional Brownian motion ⋮ Setvalued dynamical systems for stochastic evolution equations driven by fractional noise ⋮ FRACTIONAL BROWNIAN MOTION AND STOCHASTIC EQUATIONS IN HILBERT SPACES

Cites Work

• Existence and uniqueness theorems for fBm stochastic differential equations
• The Ljusternik-Schnirelman theory for indefinite and not necessarily odd nonlinear operators and its applications
• Stochastic analysis of fractional brownian motions
• Parabolic regularzation of a first order stochastic partial differential equation
• Fractional Brownian Motions, Fractional Noises and Applications
• Stochastic evolution equations
• Stochastic Equations in Infinite Dimensions

This page was built for publication: A parabolic stochastic differential equation with fractional Brownian motion input