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Statistics of an Appealing Class of Random Processes

Statistics of an Appealing Class of Random Processes

Shaival Hemant Nagarsheth, Shambhu Nath Sharma
Copyright: © 2021 |Pages: 17
ISBN13: 9781799847069|ISBN10: 1799847063|ISBN13 Softcover: 9781799854937|EISBN13: 9781799847076
DOI: 10.4018/978-1-7998-4706-9.ch010
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MLA

Nagarsheth, Shaival Hemant, and Shambhu Nath Sharma. "Statistics of an Appealing Class of Random Processes." Analyzing Data Through Probabilistic Modeling in Statistics, edited by Dariusz Jacek Jakóbczak, IGI Global, 2021, pp. 260-276. https://doi.org/10.4018/978-1-7998-4706-9.ch010

APA

Nagarsheth, S. H. & Sharma, S. N. (2021). Statistics of an Appealing Class of Random Processes. In D. Jakóbczak (Ed.), Analyzing Data Through Probabilistic Modeling in Statistics (pp. 260-276). IGI Global. https://doi.org/10.4018/978-1-7998-4706-9.ch010

Chicago

Nagarsheth, Shaival Hemant, and Shambhu Nath Sharma. "Statistics of an Appealing Class of Random Processes." In Analyzing Data Through Probabilistic Modeling in Statistics, edited by Dariusz Jacek Jakóbczak, 260-276. Hershey, PA: IGI Global, 2021. https://doi.org/10.4018/978-1-7998-4706-9.ch010

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Abstract

The white noise process, the Ornstein-Uhlenbeck process, and coloured noise process are salient noise processes to model the effect of random perturbations. In this chapter, the statistical properties, the master's equations for the Brownian noise process, coloured noise process, and the OU process are summarized. The results associated with the white noise process would be derived as the special cases of the Brownian and the OU noise processes. This chapter also formalizes stochastic differential rules for the Brownian motion and the OU process-driven vector stochastic differential systems in detail. Moreover, the master equations, especially for the coloured noise-driven stochastic differential system as well as the OU noise process-driven, are recast in the operator form involving the drift and modified diffusion operators involving an additional correction term to the standard diffusion operator. The results summarized in this chapter will be useful for modelling a random walk in stochastic systems.

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