Abstract
The generalized Langevin equation describes processes in a mechanical system with both deterministic and random forces which have comparable magnitudes (i.e., neither the deterministic nor random part can be neglected) and the random force is a transformed white noise. Examples of such processes are well known in physics. In this chapter, we use integral operators with Riemannian parallel translation in order to study the Langevin equations arising in geometric mechanics. Note that in the case under consideration the trajectories of the process are a.s. smooth. This makes the analysis of such systems technically much simpler than that of the general ones studied in Chap. 4.
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© 1997 Springer Science+Business Media New York
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Gliklikh, Y. (1997). The Langevin Equation. In: Global Analysis in Mathematical Physics. Applied Mathematical Sciences, vol 122. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1866-1_5
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DOI: https://doi.org/10.1007/978-1-4612-1866-1_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7317-2
Online ISBN: 978-1-4612-1866-1
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