Journal ArticleDOI
Projection operator method applied to stochastic linear differential equations
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TLDR
In this article, a projection operator which reduces quantities to their expectation value is introduced and an exact integro-differential equation for the expectation value of the stochastic process is derived.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 1974-06-01. It has received 96 citations till now. The article focuses on the topics: Stochastic differential equation & Partial differential equation.read more
Citations
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Stochastic differential equations
TL;DR: In this article, the authors define stochastic differential equations (SDEs) and their occurrence in physics, and present an alternative treatment, applicable only in a special case, but not confined to small ατ c.
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Gaussian stochastic processes in physics
TL;DR: In this paper, the authors present a generalization of the Langevin equation for the canonical density matrix and show that the generalized Langevin equations can be used to obtain the Doob-Ito-Stratonovich calculi.
Journal ArticleDOI
A cumulant expansion for stochastic linear differential equations. I
TL;DR: In this paper, a systematic expansion for the expectation value of a stochastic process is given, where the expansion parameter is the product of the magnitude of the fluctuations and their auto-correlation time.
Journal ArticleDOI
Time-convolutionless projection operator formalism for elimination of fast variables. Applications to Brownian motion
S. Chaturvedi,F. Shibata +1 more
TL;DR: In this paper, the relation between the time-convolutionless projection operator formalism and the methods developed by Kubo and van Kampen in the context of linear stochastic differential equations is discussed in detail.
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Path-integral formulation for stochastic processes driven by colored noise
TL;DR: In this paper, a detailed discussion of the path-integral formalism for stochastic processes described by a nonwhite noise is given, and the stationary distribution of the process in the weak noise limit is obtained from the Lagrangian without relying on the use of Fokker-Planck or Markovian approximations.
References
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Lectures in Theoretical Physics
Journal ArticleDOI
A cumulant expansion for stochastic linear differential equations. I
TL;DR: In this paper, a systematic expansion for the expectation value of a stochastic process is given, where the expansion parameter is the product of the magnitude of the fluctuations and their auto-correlation time.
Journal ArticleDOI
Stochastically perturbed fields, with applications to wave propagation in random media
TL;DR: In this paper, the statistical properties of a classical field propagating through a randomly inhomogeneous medium are analysed by a method in which the random medium is described by the two-point (bilocal) correlation function of its random characteristic, e.g., refractive index, potential, convective velocity, etc.