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- W1523274809 abstract "This chapter describes stochastic equations with the Markovian fluctuations of parameters. The methods based on approximating the fluctuating parameters with the Markovian random processes and fields with a finite temporal correlation radius are widely used. Such approximations can be found as solutions to the dynamic equations with delta-correlated parameter fluctuations. The problem on the statistical description of an oscillator with fluctuating frequency as a simple example of the linear dynamic system is analyzed. The one-dimensional motion of a particle, filed under the condition, that random forces have a finite temporal correlation radius is elaborated. The solutions to certain class of partial differential equations can be treated as the result of averaging certain functional over the random process delta-correlated in time. It is found that the finite-dimensional approximation of the Gaussian Markovian process is practicable for describing fluctuations of dynamic systems. The Markovian processes with finite-dimensional phase space are also elaborated." @default.
- W1523274809 created "2016-06-24" @default.
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- W1523274809 date "2011-01-01" @default.
- W1523274809 modified "2023-09-25" @default.
- W1523274809 title "Stochastic Equations with the Markovian Fluctuations of Parameters" @default.
- W1523274809 doi "https://doi.org/10.1016/b978-0-12-384966-3.00007-6" @default.
- W1523274809 hasPublicationYear "2011" @default.
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