Consider the model of random evolution on the real line consisting in a Brownian motion with alternating drift, where the random times separating consecutive reversals of the drift perform an alternating renewal process. This model arises as a suitable extension of the standard Brownian motion and of a motion at constant speed on the real line, whose direction is reversed at every event of a Poisson process. We obtain the probability law of the resulting stochastic process, with explicit expressions of the transition densities in the special case of exponentially distributed inter-renewal times.

On Brownian motions with alternating drifts

DI CRESCENZO, Antonio
2000-01-01

Abstract

Consider the model of random evolution on the real line consisting in a Brownian motion with alternating drift, where the random times separating consecutive reversals of the drift perform an alternating renewal process. This model arises as a suitable extension of the standard Brownian motion and of a motion at constant speed on the real line, whose direction is reversed at every event of a Poisson process. We obtain the probability law of the resulting stochastic process, with explicit expressions of the transition densities in the special case of exponentially distributed inter-renewal times.
2000
9783852061511
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/1058969
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