相关论文: Asymptotic behaviour of first passage time distrib…
Let $X$ be a real valued L\'evy process that is in the domain of attraction of a stable law without centering with norming function $c.$ As an analogue of the random walk results in \cite{vw} and \cite{rad} we study the local behaviour of…
Let X_t be a subordinate Brownian motion, and suppose that the Levy measure of the underlying subordinator has completely monotone density. Under very mild conditions, we find integral formulae for the tail distribution P(\tau_x > t) of…
The first-exit time process of an inverse Gaussian L\'evy process is considered. The one-dimensional distribution functions of the process are obtained. They are not infinitely divisible and the tail probabilities decay exponentially. These…
Stable subordinators, and more general subordinators possessing power law probability tails, have been widely used in the context of subdiffusions, where particles get trapped or immobile in a number of time periods, called constant…
In this paper the running average of a subordinator with a tempered stable distribution is considered. We investigate a family of previously unexplored infinite-activity subordinators induced by the probability distribution of the running…
In this article densities (and their derivatives) of subordinators and inverse subordinators are considered. Under minor restrictions, generally milder than the existing in the literature, using a useful modification of the saddle point…
As a first step in the first passage problem for passive tracer in stratified porous media, we consider the case of a two-dimensional system consisting of two layers with different convection velocities. Using a lattice generating function…
We study a first passage time of a L\'evy process over a positive constant level. In the spectrally negative case we give conditions for absolutely continuity of the distributions of the first passage times. The tail asymptotics of their…
In this note we generalise the Phillips theorem on the subordination of Feller processes by Levy subordinators to the class of additive subordinators (i.e. subordinators with independent but possibly nonstationary increments). In the case…
In this paper, we discuss estimates on transition densities for subordinators, which are global in time. We establish the sharp two-sided estimates on the transition densities for subordinators whose L\'evy measures are absolutely…
We provide exact large-time equivalents of the density and upper tail distributions of the exponential functional of a subordinator in terms of its Laplace exponents. This improves previous results on the logarithmic asymptotic behaviour of…
We consider the first-hitting time of a tempered $\beta$-stable subordinator, also called inverse tempered stable (ITS) subordinator. The density function of the ITS subordinator is obtained, for the index of stability $\beta \in (0,1)$.…
We obtain the first passage time density for a L\'{e}vy flight random process from a subordination scheme. By this method, we infer the asymptotic behavior directly from the Brownian solution and the Sparre Andersen theorem, avoiding…
We derive the asymptotic first passage time (FPT) distribution for space-dependent variable-order time-fractional diffusion, where the fractional exponent $\alpha(x)$ varies with position. For any sufficiently smooth $\alpha(x)$ on a finite…
The distribution of the first positive position reached by a random walker starting from the origin is fundamental for understanding the statistics of extremes and records in one-dimensional random walks. We present a comprehensive study of…
The first passage time process of a L\'evy subordinator with heavy-tailed L\'evy measure has long-range dependent paths. The random fluctuations that appear under two natural schemes of summation and time scaling of such stochastic…
In this paper we investigate the long time behavior of solutions to fractional in time evolution equations which appear as results of random time changes in Markov processes. We consider inverse subordinators as random times and use the…
The concept of a L\'evy subordinator is generalized to a family of non-decreasing stochastic processes, which are parameterized in terms of two Bernstein functions. Whereas the independent increments property is only maintained in the…
We consider the passage time problem for L\'evy processes, emphasising heavy tailed cases. Results are obtained under quite mild assumptions, namely, drift to $-\infty$ a.s. of the process, possibly at a linear rate (the finite mean case),…
This paper provides an exact simulation algorithm for the sampling from the joint law of the first-passage time, the undershoot and the overshoot of a subordinator crossing a non-increasing boundary. We prove that the running time of this…