Getting a stochastic process from a conservative Lagrangian: A first approach

J.E. Ramírez, J.N. Herrera and M.I. Martínez

Physica A: Statistical Mechanics and its Applications, 2016, vol. 448, issue C, 1-9

Abstract: The transition probability PV for a stochastic process generated by a conservative Lagrangian L=L0−εV is obtained at first order from a perturbation series found using a path integral. This PV corresponds to the transition probability for a random walk with a probability density given by the sum of a normal distribution and a perturbation which may be understood as the contribution of the interaction of the random walk with the external field. It is also found that the moment-generating function for PV can be expressed as the generating function of a normal distribution modified by a perturbation. Applications of these results to a linear potential, a harmonic oscillator potential, and an exponentially decaying potential are shown.

Keywords: Stochastic processes; Random walks; Classical Lagrangian; Path integral (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:448:y:2016:i:c:p:1-9

DOI: 10.1016/j.physa.2015.12.067

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