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Article

Towards Generic Simulation for Demanding Stochastic Processes

Department of Water Resources and Environmental Engineering, School of Civil Engineering, National Technical University of Athens, 15780 Athens, Greece
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Academic Editors: Claus Jacob, Ahmad Yaman Abdin and Wenhao Gui
Received: 24 May 2021 / Revised: 28 August 2021 / Accepted: 1 September 2021 / Published: 6 September 2021
(This article belongs to the Special Issue Feature Papers 2021 Editors Collection)
We outline and test a new methodology for genuine simulation of stochastic processes with any dependence structure and any marginal distribution. We reproduce time dependence with a generalized, time symmetric or asymmetric, moving-average scheme. This implements linear filtering of non-Gaussian white noise, with the weights of the filter determined by analytical equations, in terms of the autocovariance of the process. We approximate the marginal distribution of the process, irrespective of its type, using a number of its cumulants, which in turn determine the cumulants of white noise, in a manner that can readily support the generation of random numbers from that approximation, so that it be applicable for stochastic simulation. The simulation method is genuine as it uses the process of interest directly, without any transformation (e.g., normalization). We illustrate the method in a number of synthetic and real-world applications, with either persistence or antipersistence, and with non-Gaussian marginal distributions that are bounded, thus making the problem more demanding. These include distributions bounded from both sides, such as uniform, and bounded from below, such as exponential and Pareto, possibly having a discontinuity at the origin (intermittence). All examples studied show the satisfactory performance of the method. View Full-Text
Keywords: stochastics; stochastic processes; stochastic simulation; Monte Carlo simulation; long range dependence; persistence; Hurst–Kolmogorov dynamics; climacogram; cumulants; intermittence stochastics; stochastic processes; stochastic simulation; Monte Carlo simulation; long range dependence; persistence; Hurst–Kolmogorov dynamics; climacogram; cumulants; intermittence
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MDPI and ACS Style

Koutsoyiannis, D.; Dimitriadis, P. Towards Generic Simulation for Demanding Stochastic Processes. Sci 2021, 3, 34. https://doi.org/10.3390/sci3030034

AMA Style

Koutsoyiannis D, Dimitriadis P. Towards Generic Simulation for Demanding Stochastic Processes. Sci. 2021; 3(3):34. https://doi.org/10.3390/sci3030034

Chicago/Turabian Style

Koutsoyiannis, Demetris, and Panayiotis Dimitriadis. 2021. "Towards Generic Simulation for Demanding Stochastic Processes" Sci 3, no. 3: 34. https://doi.org/10.3390/sci3030034

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