相关论文: Complete monotonicity of time-changed L\'evy proce…

We investigate the first-passage dynamics of symmetric and asymmetric L\'evy flights in a semi-infinite and bounded intervals. By solving the space-fractional diffusion equation, we analyse the fractional-order moments of the first-passage…

Consider a Markov chain with finite state $\{0, 1, ..., d\}$. We give the generation functions (or Laplace transforms) of absorbing (passage) time in the following two situations : (1) the absorbing time of state $d$ when the chain starts…

This paper is a continuation a previous work of the authors where parametric Gevrey asymptotics for singularly perturbed nonlinear PDEs has been studied. Here, the partial differential operators are combined with particular Moebius…

Distributional properties -including Laplace transforms- of integrals of Markov processes received a lot of attention in the literature. In this paper, we complete existing results in several ways. First, we provide the analytical solution…

Let $u(s,t)$ be a continuous potential density of a symmetric L\'evy process or diffusion with state space $T$ killed at $T_{0}$, the first hitting time of $0$, or at $\lambda \wedge T_{0}$, where $\lambda$ is an independent exponential…

In this paper, we study the existence of the transition densities of one-dimensional L\'evy processes. Compared with past results, our results contain the L\'evy processes whose L\'evy symbols have logarithm behavior at infinity. Our…

The Lamperti correspondence gives a prominent role to two random time changes: the exponential functional of a L\'evy process drifting to $\infty$ and its inverse, the clock of the corresponding positive self-similar process. We describe…

Motivated by classical considerations from risk theory, we investigate boundary crossing problems for refracted L\'evy processes. The latter is a L\'evy process whose dynamics change by subtracting off a fixed linear drift (of suitable…

Continuous-state branching processes (CSBPs) with immigration (CBIs), stopped on hitting zero, are generalized by allowing the process governing immigration to be any L\'evy process without negative jumps. Unlike the CBIs, these newly…

We prove that certain quotients of entire functions are characteristic functions. Under some conditions, the probability measure corresponding to a characteristic function of that type has a density which can be expressed as a generalized…

In this paper, we will discuss an approximation of the characteristic function of the first passage time for a Levy process using the martingale approach. The characteristic function of the first passage time of the tempered stable process…

We establish that a mode-coupling approximation for the dynamics of multi-component systems obeying Smoluchowski dynamics preserves a subtle yet fundamental property: the matrices of partial density correlation functions are completely…

For a continuous-time Bienaym\'e-Galton-Watson process, $X$, with immigration and culling, $0$ as an absorbing state, call $X^q$ the process that results from killing $X$ at rate $q\in (0,\infty)$, followed by stopping it on extinction or…

Numerous studies grounded on Hawkes processes have been carried out in many fields including finance, biology and social network. Hawkes processes form a class of selfexciting simple point processes. In this article, we consider a general…

We investigate the upper tail probabilities of the all-time maximum of a stable L\'evy process with a power negative drift. The asymptotic behaviour is shown to be exponential in the spectrally negative case and polynomial otherwise, with…

We study the properties of the exponential functional $\int\_0^{+ \infty} e^{- X^{\uparrow} (t)}dt$ where $X^{\uparrow}$ is a spectrally one-sided L{\'e}vy process conditioned to stay positive. In particular, we study finiteness,…

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…

We consider exponential functionals of a multi-dimensional Brownian motion with drift, defined via a collection of linear functionals. We give a characterization of the Laplace transform of their joint law as the unique bounded solution, up…

We revisit the Bieberbach conjecture in the framework of SLE processes and, more generally, L\'evy processes. The study of their unbounded whole-plane versions leads to a discrete series of exact results for the expectations of coefficients…

Let $\{D(s), s \geq 0 \}$ be a L\'evy subordinator, that is, a non-decreasing process with stationary and independent increments and suppose that $D(0) = 0$. We study the first-hitting time of the process $D$, namely, the process $E(t) =…