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Stochastic Lagrangians for noisy dynamics

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  • Materassi, Massimo

Abstract

The dynamical variables ψ of a classical system, undergoing stochastic stirring forces, satisfy equations of motion with noise terms. Hence, these ψ show a stochastic evolution themselves. The probability of each possible realization of ψ within a given time interval, arises from the interplay between the deterministic parts of dynamics and the statistics of noise terms. In this work, we discuss the construction of the stochastic Lagrangian out of the dynamical equations, that is a tool to calculate the realization probabilities of the variables ψ as path integrals.

Suggested Citation

  • Materassi, Massimo, 2020. "Stochastic Lagrangians for noisy dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    • Handle: RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920301156
    DOI: 10.1016/j.chaos.2020.109713
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    References listed on IDEAS

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    1. Misra, B. & Prigogine, I. & Courbage, M., 1979. "From deterministic dynamics to probabilistic descriptions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 98(1), pages 1-26.
    2. Materassi, Massimo, 2019. "Stochastic field theory for the ionospheric fluctuations in Equatorial Spread F," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 186-210.
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