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• W2927337132 abstract "We study the non-Markovian random continuous processes described by the Mori-Zwanzig equation. As a starting point, we use the Markovian Gaussian Ornstein-Uhlenbeck process and introduce an integral memory term depending on the past of the process into an expression for the higher-order transition probability function and the stochastic differential equation. We show that the proposed processes can be considered as continuous-time interpolations of discrete-time higher-order autoregressive sequences. An equation connecting the memory function (the kernel of integral term) and the two-point correlation function is obtained. A condition for stationarity of the process is established. We suggest a method to generate stationary continuous stochastic processes with a prescribed pair correlation function. As an illustration, some examples of numerical simulation of the processes with nonlocal memory are presented." @default.
• W2927337132 created "2019-04-11" @default.
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• W2927337132 date "2019-11-26" @default.
• W2927337132 modified "2023-10-16" @default.
• W2927337132 title "Continuous stochastic processes with nonlocal memory" @default.
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• W2927337132 doi "https://doi.org/10.1103/physreve.100.052141" @default.
• W2927337132 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/31869899" @default.
• W2927337132 hasPublicationYear "2019" @default.
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