On the stochastic pendulum with Ornstein-Uhlenbeck noise

Kirone Mallick; Philippe Marcq

doi:10.1088/0305-4470/37/17/008

On the stochastic pendulum with Ornstein-Uhlenbeck noise

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Abstract

We study a frictionless pendulum subject to multiplicative random noise. Because of destructive interference between the angular displacement of the system and the noise term, the energy fluctuations are reduced when the noise has a non-zero correlation time. We derive the long time behaviour of the pendulum in the case of Ornstein-Uhlenbeck noise by a recursive adiabatic elimination procedure. An analytical expression for the asymptotic probability distribution function of the energy is obtained and the results agree with numerical simulations. Lastly, we compare our method with other approximation schemes.

Original language	English
Pages (from-to)	4769-4785
Number of pages	17
Journal	Journal of Physics A: Mathematical and General
Volume	37
Issue number	17
DOIs	https://doi.org/10.1088/0305-4470/37/17/008
Publication status	Published - 30 Apr 2004
Externally published	Yes

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title = "On the stochastic pendulum with Ornstein-Uhlenbeck noise",

abstract = "We study a frictionless pendulum subject to multiplicative random noise. Because of destructive interference between the angular displacement of the system and the noise term, the energy fluctuations are reduced when the noise has a non-zero correlation time. We derive the long time behaviour of the pendulum in the case of Ornstein-Uhlenbeck noise by a recursive adiabatic elimination procedure. An analytical expression for the asymptotic probability distribution function of the energy is obtained and the results agree with numerical simulations. Lastly, we compare our method with other approximation schemes.",

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AU - Mallick, Kirone

AU - Marcq, Philippe

PY - 2004/4/30

Y1 - 2004/4/30

N2 - We study a frictionless pendulum subject to multiplicative random noise. Because of destructive interference between the angular displacement of the system and the noise term, the energy fluctuations are reduced when the noise has a non-zero correlation time. We derive the long time behaviour of the pendulum in the case of Ornstein-Uhlenbeck noise by a recursive adiabatic elimination procedure. An analytical expression for the asymptotic probability distribution function of the energy is obtained and the results agree with numerical simulations. Lastly, we compare our method with other approximation schemes.

AB - We study a frictionless pendulum subject to multiplicative random noise. Because of destructive interference between the angular displacement of the system and the noise term, the energy fluctuations are reduced when the noise has a non-zero correlation time. We derive the long time behaviour of the pendulum in the case of Ornstein-Uhlenbeck noise by a recursive adiabatic elimination procedure. An analytical expression for the asymptotic probability distribution function of the energy is obtained and the results agree with numerical simulations. Lastly, we compare our method with other approximation schemes.

U2 - 10.1088/0305-4470/37/17/008

DO - 10.1088/0305-4470/37/17/008

M3 - Article

AN - SCOPUS:2442522140

SN - 0305-4470

VL - 37

SP - 4769

EP - 4785

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 17

ER -

On the stochastic pendulum with Ornstein-Uhlenbeck noise

Abstract

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