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A Symmetry-Based Approach for First-Passage-Times of Gauss-Markov Processes through Daniels-Type Boundaries

Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli Federico II, 80126 Napoli, Italy
Symmetry 2020, 12(2), 279; https://doi.org/10.3390/sym12020279 (registering DOI)
Received: 14 January 2020 / Revised: 4 February 2020 / Accepted: 6 February 2020 / Published: 13 February 2020
Symmetry properties of the Brownian motion and of some diffusion processes are useful to specify the probability density functions and the first passage time density through specific boundaries. Here, we consider the class of Gauss-Markov processes and their symmetry properties. In particular, we study probability densities of such processes in presence of a couple of Daniels-type boundaries, for which closed form results exit. The main results of this paper are the alternative proofs to characterize the transition probability density between the two boundaries and the first passage time density exploiting exclusively symmetry properties. Explicit expressions are provided for Wiener and Ornstein-Uhlenbeck processes. View Full-Text
Keywords: symmetry functions; transition probability density function; first-exit-time; two-sided region; diffusion processes symmetry functions; transition probability density function; first-exit-time; two-sided region; diffusion processes
MDPI and ACS Style

Pirozzi, E. A Symmetry-Based Approach for First-Passage-Times of Gauss-Markov Processes through Daniels-Type Boundaries. Symmetry 2020, 12, 279.

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