We consider a fractional Ornstein-Uhlenbeck process involving a stochastic forcing term in
the drift, as a solution of a linear stochastic differential equation driven by a fractional …

We consider the area functional defined by the integral of an Ornstein–Uhlenbeck process
which starts from a given value and ends at the time it first reaches zero (its equilibrium …

We investigate the main statistical parameters of the integral over time of the fractional
Brownian motion and of a kind of pseudo-fractional Gaussian process, obtained as a …

We investigate the stochastic processes obtained as the fractional Riemann-Liouville
integral of order α∈(0, 1) of Gauss-Markov processes. The general expressions of the …

Abstract For Ornstein-Uhlenbeck process X (t), starting from X (0)= x> 0, we highlight some
results about the first-passage time of X (t) through zero and its first-passage area, that is the …

A modified LIF-type stochastic model is considered with a non-delta correlated stochastic
process in place of the traditional white noise. Two different mechanisms of reset are …

Abstract The Ornstein–Uhlenbeck process is a Gaussian process with applications in
various fields, originally as a model for the velocity of a Brownian particle subject to friction …

Let d X (t)= Y (t) dt, where Y (t) is an Ornstein–Uhlenbeck process with Poissonian jumps,
and let T (x, y) be the first time that X (t)+ Y (t)= 0, given that X (0)= x and Y (0)= y. The …

We consider the process V (t): t≥ 0 defined by V (t)= v 0 e X (t)(for all t≥ 0), where v 0> 0
and X (t): t≥ 0 is a compound Poisson process with exponentially distributed jumps and a …

We investigate the stochastic processes obtained as the fractional Riemann-Liouville
integral of order $\alpha\in (0, 1) $ of Gauss-Markov processes. The general expressions of …