General approach to filtering with fractional brownian noises — application to linear systems

DOI10.1080/17442500008834261zbMath0979.93117OpenAlexW2015782645MaRDI QIDQ2706908

M.-C. Roubaud, Marina Kleptsyna, Alain Le Breton

Publication date: 2 July 2001

Published in: Stochastics and Stochastic Reports (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17442500008834261

zbMATH Keywords

integral representationfilteringinnovation processfractional Bronian motionKalman equations

Mathematics Subject Classification ID

Filtering in stochastic control theory (93E11) Signal detection and filtering (aspects of stochastic processes) (60G35) Generalized stochastic processes (60G20)

Related Items

Unnamed Item ⋮ Local asymptotic normality and estimation via Kalman-Bucy filter for linear systems driven by fractional Brownian motions ⋮ Linear Filtering with Fractional Noises: Large Time and Small Noise Asymptotics ⋮ Kalman type filter under stationary noises ⋮ Insider trading equilibrium in a market with memory ⋮ Large deviations for optimal filtering with fractional Brownian motion ⋮ Solving SPDEs driven by colored noise: A chaos approach ⋮ Asymptotic expansions of solutions of stochastic differential equations driven by multivariate fractional Brownian motions having Hurst indices greater than 1/3 ⋮ Insider trading with memory under random deadline ⋮ About the linear-quadratic regulator problem under a fractional Brownian perturbation ⋮ Stochastic integrals and evolution equations with Gaussian random fields ⋮ Nonlinear Filtering with Fractional Brownian Motion Noise ⋮ Linear filtering of systems with memory and application to finance ⋮ Separation principle in the fractional Gaussian linear-quadratic regulator problem with partial observation ⋮ Sequential Testing for Simple Hypotheses for Processes Driven by Fractional Brownian Motion ⋮ Maximum Likelihood Estimation in Partially Observed Stochastic Differential System Driven by a Fractional Brownian Motion ⋮ Effective signal extraction via local polynomial approximation under long-range dependency conditions ⋮ Insurance control for classical risk model with fractional Brownian motion perturbation ⋮ On the infinite time horizon linear-quadratic regulator problem under a fractional Brownian perturbation ⋮ On the anticipative nonlinear filtering problem and its stability

Cites Work

• Filtering and parameter estimation in a simple linear system driven by a fractional Brownian motion
• Stochastic analysis of the fractional Brownian motion
• An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions
• Differential equations driven by rough signals. I: An extension of an inequality of L. C. Young
• Linear filtering with fractional brownian motion
• Une approche de type girsanov pour le filtrage dans un système linéaire simple avec bruit brownien fractionnaire
• Stochastic analysis of fractional brownian motions
• On the prediction of fractional Brownian motion
• On the optimal filtering of diffusion processes
• Fractional Brownian Motions, Fractional Noises and Applications
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item