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Article

On the Simulation of a Special Class of Time-Inhomogeneous Diffusion Processes

Dipartimento di Informatica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Fisciano, SA, Italy
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Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Andrea Scapellato
Mathematics 2021, 9(8), 818; https://doi.org/10.3390/math9080818
Received: 3 February 2021 / Revised: 30 March 2021 / Accepted: 8 April 2021 / Published: 9 April 2021
(This article belongs to the Special Issue Stochastic Statistics and Modeling)
General methods to simulate probability density functions and first passage time densities are provided for time-inhomogeneous stochastic diffusion processes obtained via a composition of two Gauss–Markov processes conditioned on the same initial state. Many diffusion processes with time-dependent infinitesimal drift and infinitesimal variance are included in the considered class. For these processes, the transition probability density function is explicitly determined. Moreover, simulation procedures are applied to the diffusion processes obtained starting from Wiener and Ornstein–Uhlenbeck processes. Specific examples in which the infinitesimal moments include periodic functions are discussed. View Full-Text
Keywords: Gauss–Markov processes; Wiener process; Ornstein–Uhlenbeck process; first-passage time densities; simulation algorithms Gauss–Markov processes; Wiener process; Ornstein–Uhlenbeck process; first-passage time densities; simulation algorithms
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MDPI and ACS Style

Giorno, V.; Nobile, A.G. On the Simulation of a Special Class of Time-Inhomogeneous Diffusion Processes. Mathematics 2021, 9, 818. https://doi.org/10.3390/math9080818

AMA Style

Giorno V, Nobile AG. On the Simulation of a Special Class of Time-Inhomogeneous Diffusion Processes. Mathematics. 2021; 9(8):818. https://doi.org/10.3390/math9080818

Chicago/Turabian Style

Giorno, Virginia, and Amelia G. Nobile. 2021. "On the Simulation of a Special Class of Time-Inhomogeneous Diffusion Processes" Mathematics 9, no. 8: 818. https://doi.org/10.3390/math9080818

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