On the First-Passage Time Problem for a Feller-Type Diffusion Process

Virginia Giorno and Amelia G. Nobile
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Virginia Giorno: Dipartimento di Informatica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Fisciano, Salerno, Italy
Amelia G. Nobile: Dipartimento di Informatica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Fisciano, Salerno, Italy

Mathematics, 2021, vol. 9, issue 19, 1-27

Abstract: We consider the first-passage time problem for the Feller-type diffusion process, having infinitesimal drift B 1 ( x , t ) = ? ( t ) x + ? ( t ) and infinitesimal variance B 2 ( x , t ) = 2 r ( t ) x , defined in the space state [ 0 , + ? ) , with ? ( t ) ? R , ? ( t ) > 0 , r ( t ) > 0 continuous functions. For the time-homogeneous case, some relations between the first-passage time densities of the Feller process and of the Wiener and the Ornstein–Uhlenbeck processes are discussed. The asymptotic behavior of the first-passage time density through a time-dependent boundary is analyzed for an asymptotically constant boundary and for an asymptotically periodic boundary. Furthermore, when ? ( t ) = ? r ( t ) , with ? > 0 , we discuss the asymptotic behavior of the first-passage density and we obtain some closed-form results for special time-varying boundaries.

Keywords: first-passage time densities; Laplace transforms; Wiener process; Ornstein-Uhlenbeck process; first-passage time moments; asymptotic behaviors (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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