On the first-passage times of certain Gaussian processes, and related asymptotics

Time-Inhomogeneous Feller-type Diffusion Process with Absorbing Boundary Condition

“…One-dimensional time-inhomogeneous diffusion processes play a relevant role in different application fields, including physics, biology, neuroscience, finance and others (cf., for instance, Giorno and Nobile [1,2], Albano and Giorno [3], Ghost and Prajneshu [4], Buonocore et al [5], Gutiérrez et al [6], Di Crescenzo et al [7], Román-Román et al [8], Molini et al [9], Gan and Waxman [10], Abundo [11]). In this paper, we consider a timeinhomogeneous Feller-type diffusion process, characterized by linear infinitesimal drift and linear infinitesimal variance vanishing in the zero-state (lower boundary of the process).…”

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

“…To include several aspects of the real phenomena, one is led to consider increasing complex processes (cf., for instance, Di Crescenzo et al [10], Giorno et al [11,12], Abundo [13], Veestraeten [14], Molini et al [15], Lim and Muniandy [16], Jeon et al [17]). In these contexts, the focus is on specific probabilistic characteristics that define the behavior of the stochastic processes as the transition distributions and the related moments as well as the first passage time through specific time-dependent boundaries.…”

“…In particular, in Di Crescenzo et al [10], and in Giorno et al [11,12], new procedures for constructing transition probability density functions and first passage time densities through constant boundaries are proposed for generally time-inhomogeneous diffusion processes. In Abundo [13], some asymptotic results for diffusions and Gauss-Markov process and their fractional integrals are obtained. In Veestraeten [14], the transition and first hitting time densities and moments for the Ornstein-Uhlenbeck process between exponential thresholds are derived.…”