This article is cited in 3 papers

Short Communications

Brownian motion with drift in a Hilbert space and its application in integration theory

A. I. Kirillov

Moscow Power Engineering Institute (Technical University)

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.

Received: 29.12.1991

 English version: Theory of Probability and its Applications, 1993, 38:3, 529–533

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