相关论文: L\'{e}vy processes and stochastic integrals in the…

This paper considers discretization of the L\'evy process appearing in the Lamperti representation of a strictly positive self-similar Markov process. Limit theorems for the resulting approximation are established under some regularity…

The univariate extreme value theory deals with the convergence in type of powers of elements of sequences of cumulative distribution functions on the real line when the power index gets infinite. In terms of convergence of random variables,…

Consider a one-sided Markov additive process with an upper and a lower barrier, where each can be either reflecting or terminating. For both defective and non-defective processes and all possible scenarios we identify the corresponding…

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…

A cylindrical Levy process does not enjoy a cylindrical version of the semi-martingale decomposition which results in the need to develop a completely novel approach to stochastic integration. In this work, we introduce a stochastic…

Using the method of Krylov's estimates, we prove the existence of weak solutions of stochastic differential equations driven by purely discontinuous Levy processes satisfying an additional assumption. The diffusion coefficient is assumed to…

This article study the class of distributions obtained by subordinating L\'evy processes and L\'evy bases. To do this we derive properties of a suitable mapping obtained via L\'evy mixing. We show that our results can be used to solve the…

This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…

We show the equivalence of three properties for an infinitely divisible distribution: the subexponentiality of the density, the subexponentiality of the density of its L\'evy measure and the tail equivalence between the density and its…

We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…

The probabilistic symbol is the right-hand side derivative of the characteristic functions corresponding to the one-dimensional marginals of a stochastic process. This object, as long as the derivative exists, provides crucial information…

We analyze confining mechanisms for L\'{e}vy flights. When they evolve in suitable external potentials their variance may exist and show signatures of a superdiffusive transport. Two classes of stochastic jump - type processes are…

The distributional support of the sample paths of L\'evy processes is an important issue for the construction of sparse statistical models, theories of integration in infinite dimensions and the existence of generalized solutions of…

We introduce and document a class of probability distributions, called bilateral generalized inverse Gaussian (BGIG) distributions, that are obtained by convolution of two generalized inverse Gaussian distributions supported by the positive…

In this paper we study the convergence of solutions for (possibly degenerate) stochastic differential equations driven by L\'evy processes, when the coefficients converge in some appropriate sense. First, we prove, by means of a…

In this paper, we study the weak convergence of the extremes of supercritical branching L\'evy processes $\{\mathbb{X}_t, t \ge0\}$ whose spatial motions are L\'evy processes with regularly varying tails. The result is drastically different…

We develop a method that relates the truncated cumulant-function of the fourth order with the L\'evian cumulant-function. This gives us explicit formulas for the L\'evy-parameters, which allow a real-time analysis of the state of a…

Conditional independence and graphical models are crucial concepts for sparsity and statistical modeling in higher dimensions. For L\'evy processes, a widely applied class of stochastic processes, these notions have not been studied. By the…

This article develops general conditions for weak convergence of adaptive Markov chain Monte Carlo processes and is shown to imply a weak law of large numbers for bounded Lipschitz continuous functions. This allows an estimation theory for…

Let $\{L(t),t\geq 0\}$ be a L\'{e}vy process with representative random variable $L(1)$ defined by the infinitely divisible logarithmic series distribution. We study here the transition probability and L\'{e}vy measure of this process. We…