Related papers: Hitting times for Gaussian processes

We derive general results on the small deviation behavior for some classes of iterated processes. This allows us, in particular, to calculate the rate of the small deviations for $n$-iterated Brownian motions and, more generally, for the…

We study the joint moments of occupation times on the legs of a diffusion spider. Specifically, we give a recursive formula for the Laplace transform of the joint moments, which extends earlier results for a one-dimensional diffusion. For a…

This paper studies hitting properties for the system of generalized fractional kinetic equations driven by Gaussian noise fractional in time and white or colored in space. We derive the mean square modulus of continuity and some second…

This paper introduces a structural equation formulation that gives rise to a new family of quasi-periodic Gaussian processes, useful to process a broad class of natural and physiological signals. The proposed formulation simplifies…

The Lamperti transform offers a powerful bridge between self-similar processes and stationary dynamics, making it especially useful for analyzing anomalous diffusion models that lack stationary increments. In this paper we examine the…

We consider a particle diffusing along the links of a general graph possessing some absorbing vertices. The particle, with a spatially-dependent diffusion constant D(x) is subjected to a drift U(x) that is defined in every point of each…

We demonstrate that a Langevin equation that describes the motion of a Brownian particle under non-equilibrium conditions can be exactly transformed to a special equation that explicitly exhibits the response of the velocity to a time…

We consider a Brownian particle moving on a ring. We study the probability distributions of the total number of turns and the net number of counter-clockwise turns the particle makes till time t. Using a method based on the renewal…

We consider a Brownian motion on a general graph, that starts at time t=0 from some vertex O and stops at time t somewhere on the graph. Denoting by g the last time when O is reached, we establish a simple expression for the Laplace…

In this article we discuss the existence of local time for a class of Gaussian processes which appears as the solutions to some stochastic evolution equations. We show that on small intervals such processes are Gaussian integrators…

We study the probability distribution of the value of geometric Brownian motion at the stochastic observation time. It is known that the exponentially distributed observation time yields the distribution called the double Pareto…

We consider shot-noise processes with an impulse response written in terms of the logarithm of the ratio between current and event time (instead of the usual absolute time difference). We study its finite-time properties as well as its weak…

Our aim in this article is to provide explicit computable estimates for the cumulative distribution function (c.d.f.) and the $p$-th order moment of the exponential functional of a fractional Brownian motion (fBM) with drift. Using…

We consider an obliquely reflected Brownian motion $Z$ with positive drift in a quadrant stopped at time $T$, where $T:=\inf \{ t>0 : Z(t)=(0,0) \}$ is the first hitting time of the origin. Such a process can be defined even in the…

The partial differential equation of Gaussian diffusion is generalized by using the time-fractional derivative of distributed order between 0 and 1, in both the Riemann-Liouville (R-L) and the Caputo (C) sense. For a general distribution of…

We consider the occupation area of spherical (fractional) Brownian motion, i.e. the area where the process is positive, and show that it is uniformly distributed. For the proof, we introduce a new simple combinatorial view on occupation…

In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…

In this short note we show that any action for $N$ interacting particles can be made invariant under gauged Galilean transformations. While resulting Lagrangian is generally very complicated its Hamiltonian has simple form with first class…

We study the persistence probability for some two-sided discrete-time Gaussian sequences that are discrete-time analogs of fractional Brownian motion and integrated fractional Brownian motion, respectively. Our results extend the…

In this paper, we introduce drifted versions of the generalized counting process (GCP) with a deterministic drift and a random drift. The composition of stable subordinator with an independent inverse stable subordinator is taken as the…