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A Note on the Long Time Asymptotics of the Brownian Motion with Application to the Theory of Quantum Measurement

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Abstract

Estimates of growth of the standard d-dimensional Brownian motion W(t) and its integral V(t) = ∫t 0 W (s) ds are obtained, as t → ∞, and an application is discussed to the long time asymptotics of the solutions of the nonlinear stochastic equation of the quantum filtering theory.

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Authors
  1. Vassili N. Kolokoltsov
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Kolokoltsov, V.N. A Note on the Long Time Asymptotics of the Brownian Motion with Application to the Theory of Quantum Measurement. Potential Analysis 7, 759–764 (1997). https://doi.org/10.1023/A:1017946519693

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  • DOI: https://doi.org/10.1023/A:1017946519693

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