Related papers: Hitting times for Gaussian processes

Fractional Brownian motion is a self-affine, non-Markovian and translationally invariant generalization of Brownian motion, depending on the Hurst exponent $H$. Here we investigate fractional Brownian motion where both the starting and the…

Firstly, we compute the distribution function for the hitting time of a linear time-dependent boundary $t\mapsto a+bt,\ a\geq 0,\,b\in \R,$ by a reflecting Brownian motion. The main tool hereby is Doob's formula which gives the probability…

For an Ornstein-Uhlenbeck process driven by a double exponential jump diffusion process, we obtain formulas for the joint Laplace transform of it and its occupation times. The approach used is remarkable and can be extended to investigate…

Local perturbations of a Brownian motion are considered. As a limit we obtain a non-Markov process that behaves as a reflected Brownian motion on the positive half line until its local time at zero reaches some exponential level, then…

In this paper, firstly, we generalize the definition of the bifractional Brownian motion $B^{H,K}:=\Big(B^{H,K}\;;\;t\geq 0\Big)$, with parameters $H\in(0,1)$ and $K\in(0,1]$, to the case where $H$ is no longer a constant, but a function…

We study the two-dimensional joint distribution of the first hitting time of a constant level by a continuous-state branching process with immigration and their primitive stopped at this time. We show an explicit expression of its Laplace…

We present an asymptotic result for the Laplace transform of the time integral of the geometric Brownian motion $F(\theta,T) = \mathbb{E}[e^{-\theta X_T}]$ with $X_T = \int_0^T e^{\sigma W_s + ( a - \frac12 \sigma^2)s} ds$, which is exact…

Under certain mild conditions, limit theorems for additive functionals of some $d$-dimensional self-similar Gaussian processes are obtained. These limit theorems work for general Gaussian processes including fractional Brownian motions,…

This article is concerned with the joint law of an integrated Wishart bridge process and the trace of an integrated inverse Wishart bridge process over the interval $ \left[0,t\right] $. Its Laplace transform is obtained by studying the…

We study well-posedness of sweeping processes with stochastic perturbations generated by a fractional Brownian motion and convergence of associated numerical schemes. To this end, we first prove new existence, uniqueness and approximation…

In the context of time-subordinated Brownian motion models, Fourier theory and methodology are proposed to modelling the stochastic distribution of time increments. Gaussian Variance-Mean mixtures and time-subordinated models are reviewed…

A Brownian time process is a Markov process subordinated to the absolute value of an independent one-dimensional Brownian motion. Its transition densities solve an initial value problem involving the square of the generator of the original…

We develop a General Fluctuation Formula for phase variables that are odd under time reversal. Simulations are used to verify the new formula.

It was shown in Mishura et al. (Stochastic Process. Appl. 123 (2013) 2353-2369), that any random variable can be represented as improper pathwise integral with respect to fractional Brownian motion. In this paper, we extend this result to…

The model consists of a signal process $X$ which is a general Brownian diffusion process and an observation process $Y$, also a diffusion process, which is supposed to be correlated to the signal process. We suppose that the process $Y$ is…

A gentle introduction to Gaussian processes (GPs). The three parts of the document consider GPs for regression, classification, and dimensionality reduction.

Given a random time, we characterize the set of martingales for which the stopping theorems still hold. We also investigate how the stopping theorems are modified when we consider arbitrary random times. To this end, we introduce some…

We consider the first hitting times of the Bessel processes. We give explicit expressions for the distribution functions and for the densities by means of the zeros of the Bessel functions. The results extend the classical ones and cover…

This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential…

We relate the convergence of time-changed processes driven by fractional equations to the convergence of corresponding Dirichlet forms. The fractional equations we dealt with are obtained by considering a general fractional operator in…