7 May 2003 Dynamical formulation of Gaussian white noise
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Proceedings Volume 5114, Noise in Complex Systems and Stochastic Dynamics; (2003) https://doi.org/10.1117/12.500170
Event: SPIE's First International Symposium on Fluctuations and Noise, 2003, Santa Fe, New Mexico, United States
Abstract
We study the connection between Hamiltonian dynamics and irreversible, stochastic equations, such as the Langevin equation. We consider a simple model of a harmonic oscillator (Brownian particle) coupled to a field (heat bath). We introduce an invertible transformation operator Λ that brings us to a new representation where dynamics is decomposed into independent Markovian components, including Brownian motion. The effects of Gaussian white noise are obtained by the non-distributive property of Λ with respect to products of dynamical variables. In this way we obtain an exact formulation of white noise effects. Our method leads to a direct link between dynamics of Poincaré nonintegrable systems, probability and stochasticity.
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Gonzalo E Ordonez, Gonzalo E Ordonez, Sungyun Kim, Sungyun Kim, } "Dynamical formulation of Gaussian white noise", Proc. SPIE 5114, Noise in Complex Systems and Stochastic Dynamics, (7 May 2003); doi: 10.1117/12.500170; https://doi.org/10.1117/12.500170
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