It is studied the first-passage time (FPT) of a time homogeneous one-dimensional diffusion,
driven by the stochastic differential equation dX (t)= μ (X (t)) dt+ σ (X (t)) dB t, X (0)= x 0 …

Let X (t) be a time-homogeneous one-dimensional diffusion process defined in I⊂ ℝ,
starting at x∈ I and let c∈ I a barrier with c< x. Suppose that, whenever the barrier c is …

A comprehensive outline is presented for obtaining the Laplace transforms of the transition
probability density functions and of the first-passage-time densities for one-dimensional time …

The asymptotic behavior of the first-passage-time pdf through a constant boundary is studied
when the boundary approaches the endpoints of the diffusion interval. We show that for a …

We explore the first passage problem for sticky reflecting diffusion processes with double
exponential jumps. The joint Laplace transform of the first passage time to an upper level …

A special class of time-inhomogeneous diffusion processes, generated starting from Gauss–
Markov processes conditioned on the same initial state, is considered. This class includes …

A two-dimensional homogeneous diffusion process with break is considered. The
distribution of the first exit point of such a process from an arbitrary neighborhood of zero as …

Let dX (t)=− Y (t) dt, where Y (t) is a one-dimensional diffusion process. First-exit problems
from C∈ R2 are studied for the degenerate two-dimensional diffusion process (X (t), Y (t)) …

We solve the Fokker-Planck equation for the Wiener process with drift in the presence of
elastic boundaries and a fixed start point. An explicit expression is obtained for the first …

Using a new technique, based on the regularisation of a càdlàg process via the double
Skorohod map, we obtain limit theorems for integrated numbers of level crossings of …