Girsanov's theorem in Hilbert space and an application to the statistics of Hilbert space-valued stochastic differential equations

DOI10.1016/0304-4149(84)90004-8zbMath0553.93059OpenAlexW2033798227MaRDI QIDQ759721

Wilfried Loges

Publication date: 1984

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(84)90004-8

zbMATH Keywords

parameter estimationGirsanov type theoremsHilbert space valued Wiener processeslinear stochastic evolution equations

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Foundations and philosophical topics in statistics (62A01) Estimation and detection in stochastic control theory (93E10) Linear systems in control theory (93C05) Control/observation systems in abstract spaces (93C25) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Inner product spaces and their generalizations, Hilbert spaces (46C99)

Related Items (10)

Estimates for invariant probability measures of degenerate SPDEs with singular and path-dependent drifts ⋮ On minimum-contrast estimation for hilbert space-valued stochastic differential equations ⋮ On asymptotic properties of maximum likelihood estimators for parabolic stochastic PDE's ⋮ Statistical inference for SPDEs: an overview ⋮ Parameter estimation in infinite-dimensional stochastic differential equations ⋮ Unique ergodicity for a class of stochastic hyperbolic equations with additive space-time white noise ⋮ Estimation of anthracnose dynamics by nonlinear filtering ⋮ Law equivalence of Ornstein-Uhlenbeck processes driven by a Lévy process ⋮ The Bernstein-von Mises theorem and spectral asymptotics of Bayes estimators for parabolic SPDEs ⋮ Asymptotic statistical inference for a stochastic heat flow problem

Cites Work

• Gaussian measures in Banach spaces
• Infinite dimensional linear systems theory
• On a Problem of Testing Hypotheses and Asymptotic Normality of Stochastic Integrals
• Infinite-dimensional elliptic operators and parabolic equations connected with them
• Stochastic Integrals Based on Martingales Taking Values in Hilbert Space
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