This article is cited in 10 papers

Two mathematical problems of canonical quantization. III. Stochastic vacuum mechanics

A. I. Kirillov

Moscow Power Engineering Institute

Abstract: The problem of recovery of the measure from its logarithmic derivative is investigated. The role of this problem in stochastic mechanics, canonical quantization, and the theory of integration of functionals is discussed. It is shown that a measure that possesses logarithmic derivative $A$ is a stationary distribution of a diffusion process with drift coefficient $A$. This makes it possible to calculate integrals with respect to the measure by means of Monte Carlo methods.

Received: 16.01.1992

 English version: Theoretical and Mathematical Physics, 1992, 91:3, 591–603

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