Related papers: Stitching pairs of Levy processes into harnesses

We study sums of independent and identically distributed random velocities in special relativity. We show that the resulting one-dimensional velocity distributions are not only stable under relativistic velocity addition but define a…

In the Hammersley harness processes the real-valued height at each site i in Z^d is updated at rate 1 to an average of the neighboring heights plus a centered random variable (the noise). We construct the process "a la Harris"…

In this paper we derive intertwining relations for a broad class of conservative particle systems both in discrete and continuous setting. Using the language of point process theory, we are able to derive a natural framework in which…

A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling…

We construct a Hunt process that can be described as an isotropic $\alpha$-stable L\'evy process reflected from the complement of a bounded open Lipschitz set. In fact, we introduce a new analytic method for concatenating Markov processes.…

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…

This work considers the problem of learning the Markov parameters of a linear system from observed data. Recent non-asymptotic system identification results have characterized the sample complexity of this problem in the single and…

In this paper we show that a non-local operator of certain type extends to the generator of a strong Markov process, admitting the transition probability density. For this transition probability density we construct the intrinsic upper and…

We consider a generalization of a one-dimensional stochastic process known in the physical literature as L\'evy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points,…

Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…

We define a new family of multivariate stochastic processes over a finite time horizon that we call Generalised Liouville Processes (GLPs). GLPs are Markov processes constructed by splitting L\'evy random bridges into non-overlapping…

We study stochastic equations of non-negative processes with jumps. The existence and uniqueness of strong solutions are established under Lipschitz and non-Lipschitz conditions. The comparison property of two solutions are proved under…

Semi-Levy process is an additive process with periodically stationary increments. In particular, it is a generalization of Levy process. The dichotomy of recurrence and transience of Levy processes is well known, but this is not necessarily…

This work explores a synchronization-like phenomenon induced by common noise for continuous-time Markov jump processes given by chemical reaction networks. A corresponding random dynamical system is formulated in a two-step procedure, at…

We consider random processes that are history-dependent, in the sense that the distribution of the next step of the process at any time depends upon the entire past history of the process. In general, therefore, the Markov property cannot…

Starting from the forward and backward infinitesimal generators of bilateral, time-homogeneous Markov processes, the self-adjoint Hamiltonians of the generalized Schroedinger equations are first introduced by means of suitable Doob…

For a broad class of the Levy processes the new form (convolution type) of the infinitesimal generators is introduced. It leads to the new notions: a truncated generator, a quasi-potential. The probability of the Levy process remaining…

By studying an admissible family of branching mechanisms introduced in Li (2014), we obtain a pruning procedure on L\'evy trees. Then we could construct a decreasing L\'evy-CRT-valued process $\{{\mathcal T}_t\}$ by pruning L\'evy trees and…

We compare two definitions of multistable L\'evy motions. Such processes are extensions of classical L\'evy motion where the stability index is allowed to vary in time. We show that the two multistable L\'evy motions have distinct…

Potential theory is a central tool to understand and analyse Markov processes. In this article, we develop its probabilistic counterpart for branching Markov chains. Specifically, we examine versions of quasi-processes or interlacements…