In this paper we use the method of images to derive the closed-form formula for the first
passage time density of a time-dependent Ornstein–Uhlenbeck process to a parametric …

We study the asymptotics of the exit probability Pε x, s {τ≤ T}, where τ is the exit time from an
open set and Pε x, s is the law of a diffusion process with a small parameter ε multiplying the …

The method earlier introduced for one-dimensional diffusion processes [6] is extended to
obtain closed form expressions for the transition pdf's of two-dimensional diffusion …

From both theoretical and applied perspectives, first passage time problems for random
processes are challenging and of great interest. In this thesis, our contribution consists on …

We review and study a one-parameter family of functional transformations, denoted by (S
(β)) β∈ ℝ, which, in the case β< 0, provides a path realization of bridges associated to the …

Let us consider a signal-plus-noise model γh (z)+ B 0 (z), z∈[0, 1], where γ> 0, h:[0, 1]→ ℝ,
and B 0 is a Brownian bridge. We establish the asymptotics for the boundary crossing …

This paper considers the absorption of a non-decreasing compound Poisson process of
finite order in a general upper boundary. The problem is relevant in fields such as risk …

C CROSSING RATES F AN VECTOR PR Karl BREITUNG Stationary Gaussian vector
processes are used to describe the behaviour of multi- Page 1 Stochastic Processes and …

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, a (t)< b (t) …

A NOTE ON DURBIN'S FORMULA FOR THE FIRST-PASSAGE DENSITY fT(t) = lim(t- s)-IE(l(s,
y)(a(s) - y(s)) lY(t ) = a(t))L.,,)(a(t)), Page 1 Statistics & Probability Letters 5 (1987) 425-428 …