Equivalence of the probability measures generated by the solutions of nonlinear evolution differential equations in a Hilbert space, disturbed by Gaussian processes. I

DOI10.1007/s10559-011-9370-yzbMath1326.60092OpenAlexW2029342399MaRDI QIDQ464984

A. D. Shatashvili, T. A. Fomina, A. A. Fomin-Shatashvili

Publication date: 30 October 2014

Published in: Cybernetics and Systems Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10559-011-9370-y

zbMATH Keywords

equivalence of probability measuresHilbert-Schmidt operatorevolution differential equationsevolution family of bounded operatorsgenerating operatorRadon-Nikodym density

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Continuity and singularity of induced measures (60G30)

Related Items

Equivalence of the probability measures generated by the solutions of nonlinear evolution differential equations in a Hilbert space, disturbed by Gaussian processes. II, Optimal estimates in problems of extrapolation, filtration, and interpolation of functionals of random processes with values in a Hilbert space

Cites Work

• Nonlinear random equations with noncoercive operators in Banach spaces
• On measures generated by equations with random coefficients
• Some necessary and sufficient conditions of the equivalence of two Gaussian measures induced by solutions of differential equations in an Euclid and a Hilbert spaces
• Defect subspaces and generalized resolvents of an Hermitian operator in the space \(\Pi_\kappa\)
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