Abstract The Onsager-Machlup (OM) functional is well known for characterizing the most
probable transition path of a diffusion process with non-vanishing noise. However, it suffers …

This paper studies the dynamics of the Ornstein–Uhlenbeck process by the deterministic
quantities such as the mean exit time and escape probability. By solving the elliptic partial …

A continuum steady-state model of oxygen transport in brain with unknown intensities of the
sources describing the oxygen inflow and its outflow via the arterioles and venules is …

Symmetry properties of the Brownian motion and of some diffusion processes are useful to
specify the probability density functions and the first passage time density through specific …

In this paper we consider a connection between the famous Skorokhod embedding problem
and the Shiryaev inverse problem for the first hitting time distribution of a Brownian motion …

We propose a simpler derivation of the probability density function of Feller Diffusion using
the Fourier Transform and solving the resulting equation via the Method of Characteristics …

We introduce a probabilistic representation of the derivative of the semigroup associated to
a multidimensional killed diffusion process defined on the half-space. The semigroup …

Let (X (t)) t≥ 0 be the pseudo-process driven by the high-order heat-type equation∂ u∂
t=±∂ Nu∂ xN, where N is an integer greater than 2. We consider the sojourn time spent by …

The probability density is a fundamental quantity for characterizing diffusion processes.
However, it is seldom known except in a few renowned cases, including Brownian motion …

Abstract Restricted Gauss–Markov processes are used to construct inhomogeneous leaky
integrate-and-fire stochastic models for single neurons activity in the presence of a lower …