On the densities of certain bounded diffusion processes

Giorno, Virginia; Nobile, Amelia Giuseppina; Ricciardi, Luigi M.

doi:10.1007/s11587-010-0097-2

Cited by 17 publications

(14 citation statements)

References 44 publications

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“…This paper aims to cover this subject considering the joint distribution between these times. Some results, presented in a recent paper by Giorno et al [12], are related with those on the Laplace transforms presented in this paper. However, their focus was not on the joint distribution of exit times from a strip.…”

Section: Introductionsupporting

confidence: 68%

“…where Proof. Generalizing the standard calculation given in [16, p. 30] for an arbitrary regular diffusion yields (12).…”

Section: System Of Integral Equationsmentioning

confidence: 82%

“…Applying the Laplace transform to (9) and using the convolution theorem we obtain (13), a result recently published in [12]. Applying the Laplace transform to (10) together with the convolution theorem for two generic points x 1 > b and x 2 < a gives the first equality in (14).…”

Section: System Of Integral Equationsmentioning

confidence: 83%

See 2 more Smart Citations

Joint Densities of First Hitting Times of a Diffusion Process Through Two Time-Dependent Boundaries

Sacerdote

Telve

Zucca

2014

Advances in Applied Probability

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Consider a one dimensional diffusion process on the diffusion interval I originated in x0 ∈ I. Let a(t) and b(t) be two continuous functions of t, t > t0 with bounded derivatives and with a(t) < b(t) and a(t), b(t) ∈ I, ∀t > t0. We study the joint distribution of the two random variables Ta and T b , first hitting times of the diffusion process through the two boundaries a(t) and b(t), respectively. We express the joint distribution of Ta, T b in terms of P (Ta < t, Ta < T b ) and P (T b < t, Ta > T b ) and we determine a system of integral equations verified by these last probabilities. We propose a numerical algorithm to solve this system and we prove its convergence properties. Examples and modeling motivation for this study are also discussed.

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Section: Introductionsupporting

confidence: 68%

“…where Proof. Generalizing the standard calculation given in [16, p. 30] for an arbitrary regular diffusion yields (12).…”

Section: System Of Integral Equationsmentioning

confidence: 82%

See 1 more Smart Citation

Joint Densities of First Hitting Times of a Diffusion Process Through Two Time-Dependent Boundaries

Sacerdote

Telve

Zucca

2014

Advances in Applied Probability

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“…1. Analytical methods to determine the Laplace transform of FPT probability density function (pdf) and its moments for time-homogeneous diffusion process and constant boundaries (cf., for instance, Darling and Siegert [1], Blake and Lindsey [2], Giorno et al [3]); 2.…”

Section: Introductionmentioning

confidence: 99%

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

Giorno

Nobile

2021

Mathematics

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We consider the first-passage time problem for the Feller-type diffusion process, having infinitesimal drift B1(x,t)=α(t)x+β(t) and infinitesimal variance B2(x,t)=2r(t)x, defined in the space state [0,+∞), with α(t)∈R, β(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 β(t)=ξr(t), with ξ>0, we discuss the asymptotic behavior of the first-passage density and we obtain some closed-form results for special time-varying boundaries.

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“…In these cases, it is necessary take into account diffusion processes with a reflecting condition in the zero state. A special diffusion process in the presence of reflecting boundaries are taken into account in Linetsky [31], Giorno et al [32,33], and Buonocore et al [34,35].…”

Section: Introductionmentioning

confidence: 99%

Restricted Gompertz-Type Diffusion Processes with Periodic Regulation Functions

Giorno

Nobile

2019

Mathematics

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We consider two different time-inhomogeneous diffusion processes useful to model the evolution of a population in a random environment. The first is a Gompertz-type diffusion process with time-dependent growth intensity, carrying capacity and noise intensity, whose conditional median coincides with the deterministic solution. The second is a shifted-restricted Gompertz-type diffusion process with a reflecting condition in zero state and with time-dependent regulation functions. For both processes, we analyze the transient and the asymptotic behavior of the transition probability density functions and their conditional moments. Particular attention is dedicated to the first-passage time, by deriving some closed form for its density through special boundaries. Finally, special cases of periodic regulation functions are discussed.

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On the densities of certain bounded diffusion processes

Cited by 17 publications

References 44 publications

Joint Densities of First Hitting Times of a Diffusion Process Through Two Time-Dependent Boundaries

Joint Densities of First Hitting Times of a Diffusion Process Through Two Time-Dependent Boundaries

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

Restricted Gompertz-Type Diffusion Processes with Periodic Regulation Functions

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