A Cameron-Martin type formula for general Gaussian processes--a filtering approach

DOI10.1080/10451120290019203zbMath1002.60031OpenAlexW2035348672MaRDI QIDQ4542934

Alain Le Breton, Marina Kleptsyna

Publication date: 3 November 2002

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

Full work available at URL: https://doi.org/10.1080/10451120290019203

zbMATH Keywords

Gaussian processmartingaleoptimal filteringfiltering errorRiccati-Volterra equation

Mathematics Subject Classification ID

Inference from stochastic processes and prediction (62M20) Gaussian processes (60G15) Martingales with continuous parameter (60G44)

Related Items (12)

Gaussian processes centered at their online average, and applications ⋮ Asymptotic properties of MLE for partially observed fractional diffusion system ⋮ \( L_2\)-small ball asymptotics for Gaussian random functions: a survey ⋮ On a family of ordinary differential equations integrable in elementary functions ⋮ Some integral equations related to random Gaussian processes ⋮ Exact small ball asymptotics in weighted \(L_2\)-norm for some Gaussian processes ⋮ Distribution of the least-squares estimators of a single Brownian trajectory diffusion coefficient ⋮ Explicit formulas for Laplace transforms of certain functionals of some time inhomogeneous diffusions ⋮ Large-time and small-ball asymptotics for quadratic functionals of Gaussian diffusions ⋮ Small ball probabilities for Gaussian random fields and tensor products of compact operators ⋮ Asymptotic properties of MLE for partially observed fractional diffusion system with dependent noises ⋮ L p estimates on a time-inhomogeneous diffusion process

Cites Work

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• On the parameter estimation of diffusional type processes with constant coefficients (elementary Gaussian processes)
• Quadratic functionals of Brownian motion
• On some examples of quadratic functionals of Brownian motion
• Quadratic functionals of brownian motion, optimal control,and the “colditz” example
• An extension of the Cameron–Martin result
• Evaluation of various Wiener integrals by use of certain Sturm-Liouville differential equations

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