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

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.