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 derivativeA is a stationary distribution of a diffusion process with drift coefficientA. This makes it possible to calculate integrals with respect to the measure by means of Monte Carlo methods.
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Additional information
Power Institute, Moscow. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 3, pp. 377–395, June, 1992.
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Kirillov, A.I. Two mathematical problems of canonical quantization. III. Stochastic vacuum mechanics. Theor Math Phys 91, 591–603 (1992). https://doi.org/10.1007/BF01017334
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DOI: https://doi.org/10.1007/BF01017334