Abstract:
Sufficient conditions are given under which a Brownian motion with drift in a Hilbert space has an invariant measure. We prove that if the measure is differentiable, then its logarithmic gradient is equal to the drift coefficient. The results obtained constitute a basis for the reconstruction of a differentiable measure from its logarithmic derivatives.
Keywords:
stochastic equation, invariant measure, ergodic properties of a differentiable measure, logarithmic derivative of a measure, reconstruction of a measure from its logarithmic derivatives.
Citation:
A. I. Kirillov, “Brownian motion with drift in a Hilbert space and its application in integration theory”, Teor. Veroyatnost. i Primenen., 38:3 (1993), 629–634; Theory Probab. Appl., 38:3 (1993), 529–533
\Bibitem{Kir93}
\by A.~I.~Kirillov
\paper Brownian motion with drift in a Hilbert space and its application in integration theory
\jour Teor. Veroyatnost. i Primenen.
\yr 1993
\vol 38
\issue 3
\pages 629--634
\mathnet{http://mi.mathnet.ru/tvp3971}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1404670}
\zmath{https://zbmath.org/?q=an:0809.60088}
\transl
\jour Theory Probab. Appl.
\yr 1993
\vol 38
\issue 3
\pages 529--533
\crossref{https://doi.org/10.1137/1138051}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1993PJ74300014}
Linking options:
https://www.mathnet.ru/eng/tvp3971
https://www.mathnet.ru/eng/tvp/v38/i3/p629
This publication is cited in the following 3 articles:
Citation in format AMSBIB
Contact us: