相关论文: Hitting times for Gaussian processes

We present a method for computing the likelihood of a mixed hitting-time model that specifies durations as the first time a latent L\'evy process crosses a heterogeneous threshold. This likelihood is not generally known in closed form, but…

Consider a negatively drifted one dimensional Brownian motion starting at positive initial position, its first hitting time to 0 has the inverse Gaussian law. Moreover, conditionally on this hitting time, the Brownian motion up to that time…

The goal of this paper is to generalize most of the moment formulae obtained in [Pri11]. More precisely, we consider a general point process \mu, and show that the relevant quantities to our problem are the so-called Papangelou intensities.…

A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral…

The three arcsine laws for Brownian motion are a cornerstone of extreme-value statistics. For a Brownian $B_t$ starting from the origin, and evolving during time $T$, one considers the following three observables: (i) the duration $t_+$ the…

We use generalized beta integrals to construct examples of Markov processes with linear regressions, and quadratic second conditional moments.

We survey existing results concerning the study in small times of the density of the solution of a rough differential equation driven by fractional Brownian motions. We also slightly improve existing results and discuss some possible…

In this article, we first establish derivative formulae for fractional Gruschin type process, which generalize the result of Wang (J Theor Probab 27:80--95, Theorem 1.1, 2012). Since we work on a non-Markovian context, some technical…

We consider so-called regular invertible Gaussian Volterra processes and derive a formula for their prediction laws. Examples of such processes include the fractional Brownian motions and the mixed fractional Brownian motions. As an…

The present paper is concerned with the integral of the absolute value of a Brownian motion with drift. By establishing an asymptotic expansion of the space Laplace transform, we obtain series representations for the probability density…

We define a time dependent empirical process based on $n$ independent fractional Brownian motions and describe strong approximations to it by Gaussian processes. They lead to strong approximations and functional laws of the iterated…

Brownian motion is the only random process which is Gaussian, stationary and Markovian. Dropping the Markovian property, i.e. allowing for memory, one obtains a class of processes called fractional Brownian motion, indexed by the Hurst…

We provide integral formulae for the Laplace transform of the entrance law of the reflected excursions for symmetric L\'evy processes in terms of their characteristic exponent. For subordinate Brownian motions and stable processes we…

We investigated the quality of forecasting of fractional Brownian motion, and new method for estimating of Hurst exponent is validated. Stochastic model of the time series in the form of converted fractional Brownian motion is proposed. The…

We give a method for computing the iterated Laplace transform of the sojourn time in an union of intervals for linear diffusion processes. This random variable comes from a model occurring in biology concerning the clustering of membrane…

We consider a wide class of increasing L\'evy processes perturbed by an independent Brownian motion as a degradation model. Such family contains almost all classical degradation models considered in the literature. Classically failure time…

We give a new procedure for generalized factorization and construction of the complete solution of strictly hyperbolic linear partial differential equations or strictly hyperbolic systems of such equations in the plane. This procedure…

Let $\{B(t), t \geq 0\}$ be a standard Brownian motion in $\mathbb{R}$. Let $T$ be the first return time to 0 after hitting 1, and $\{L(T,x), x \in \mathbb{R}\}$ be the local time process at time $T$ and level $x$. The distribution of…

We consider the paths of a Gaussian random process $x(t)$, $x(0)=0$ not exceeding a fixed positive level over a large time interval $(0,T)$, $T\gg 1$. The probability $p(T)$ of such event is frequently a regularly varying function at…

Let $T_1^{(\mu)}$ be the first hitting time of the point 1 by the Bessel process with index $\mu\in \R$ starting from $x>1$. Using an integral formula for the density $q_x^{(\mu)}(t)$ of $T_1^{(\mu)}$, obtained in Byczkowski, Ryznar (Studia…