Related papers: Logarithmic L\'{e}vy process directed by Poisson s…
Let $X$ be a L\'evy process with absolutely continuous L\'evy measure $\nu$. Small time polynomial expansions of order $n$ in $t$ are obtained for the tails $P(X_{t}\geq{}y)$ of the process, assuming smoothness conditions on the L\'evy…
In this paper we consider a ring of $N\ge 1$ queues served by a single server in a cyclic order. After having served a queue (according to a service discipline that may vary from queue to queue), there is a switch-over period and then the…
When is it possible to interpret a given Markov process as a L\'evy-like process? Since the class of L\'evy processes can be defined by the relation between transition probabilities and convolutions, the answer to this question lies in the…
Let $(U_t,V_t)$ be a bivariate L\'evy process, where $V_t$ is a subordinator and $U_t$ is a L\'evy process formed by randomly weighting each jump of $V_t$ by an independent random variable $X_t$ having cdf $F$. We investigate the asymptotic…
We describe basic motivations behind quantum or noncommutative probability, introduce quantum L\'evy processes on compact quantum groups, and discuss several aspects of the study of the latter in the example of quantum permutation groups.…
In this paper, we study the compressibility of random processes and fields, called generalized L\'evy processes, that are solutions of stochastic differential equations driven by $d$-dimensional periodic L\'evy white noises. Our results are…
This article deals with IDT processes, i.e. processes which are infinitely divisible with respect to time. Given an IDT process $(X_{t},\,t\geq0)$, there exists a unique (in law) L\'evy process $(L_{t}; t\geq0)$ which has the same…
In this paper, we are concerned with the stochastic process \begin{equation} \beta_{n}(q_{t},t)=\beta_{n}(t)=\frac{1}{\sqrt{n}}\sum_{j=1}^{n}\left\{G_{t,n}(Y(t))-G_{t}(Y_{j}(t))\right\} q_{t}(Y_{j}(t)), \tag{A} \end{equation} where for…
For a spectrally negative L\'evy process $X$, we study the following distribution: $$ \mathbb{E}_x \left[ \mathrm{e}^{- q \int_0^t \mathbf{1}_{(a,b)} (X_s) \mathrm{d}s } ; X_t \in \mathrm{d}y \right], $$ where $-\infty \leq a < b < \infty$,…
Resetting a stochastic process is an important problem describing the evolution of physical, biological and other systems which are continually returned to their certain fixed point. We consider the motion of a subdiffusive particle with a…
We present an exact sampling method for the first passage event of a Levy process. The idea is to embed the process into another one whose first passage event can be sampled exactly, and then recover the part belonging to the former from…
In this paper, we consider a type of time-changed Markov process, where the time-change is an inverse killed subordinator. This can be seen as an extension of Chen (Chen, Z., Time fractional equations and probabilistic representation, Chaos…
For $n$ equidistant observations of a L\'evy process at time distance $\Delta_n$ we consider the problem of testing hypotheses on the volatility, the jump measure and its Blumenthal-Getoor index in a non- or semiparametric manner.…
We show that exact sampling of the first passage event can be done for a Levy process with unbounded variation, if the process can be embedded in a subordinated standard Brownian motion. By sampling a series of first exit events of the…
The purpose of this paper is to construct the law of a L\'evy process conditioned to avoid zero, under mild technicals conditions, two of them being that the point zero is regular for itself and the L\'evy process is not a compound Poisson…
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…
We construct in the small-time setting the upper and lower estimates for the transition probability density of a L\'evy process in $\rn$. Our approach relies on the complex analysis technique and the asymptotic analysis of the inverse…
We consider Malliavin calculus based on the It\^o chaos decomposition of square integrable random variables on the L\'evy space. We show that when a random variable satisfies a certain measurability condition, its differentiability and…
This paper provides a framework for investigations in fluctuation theory for L\'evy processes with matrix-exponential jumps. We present a matrix form of the components of the infinitely divisible factorization. Using this representation we…
We consider two-dimensional L\'evy processes reflected to stay in the positive quadrant. Our focus is on the non-standard regime when the mean of the free process is negative but the reflection vectors point away from the origin, so that…