Related papers: G-L\'{e}vy Processes under Sublinear Expectations

The program of studying general nonlinear Markov processes was put forward in V. N. Kolokoltsov "Nonlinear Markov Semigroups and Interacting L\'evy Type Processes" (Journ. Stat. Physics 126:3 (2007), 585-642), and was developed by the…

We discuss an impact of various (path-wise) reflection-from-the barrier scenarios upon confining properties of a paradigmatic family of symmetric $\alpha $-stable L\'{e}vy processes, whose permanent residence in a finite interval on a line…

We present an existence result for L\'evy-type processes which requires only weak regularity assumptions on the symbol $q(x,\xi)$ with respect to the space variable $x$. Applications range from existence and uniqueness results for…

In the recent paper \cite{Ng5} we have introduced a method of studying the multi-dimensional Kingman convolutions and their associated stochastic processes by embedding them into some multi-dimensional ordinary convolutions which allows to…

By using lower bound conditions of the L\'evy measure, derivative formulae and Harnack inequalities are derived for linear stochastic differential equations driven by L\'evy processes. As applications, explicit gradient estimates and heat…

We suppose that a L\'evy process is observed at discrete time points. A rather general construction of minimum-distance estimators is shown to give consistent estimators of the L\'evy-Khinchine characteristics as the number of observations…

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…

We introduce diffusions on a space of interval partitions of the unit interval that are stationary with the Poisson-Dirichlet laws with parameters $(\alpha,0)$ and $(\alpha,\alpha)$. The construction has two steps. The first is a general…

For a general free L\'evy process, we prove the existence of its higher variation processes as limits in distribution, and identify the limits in terms of the L\'evy-It\^o representation of the original process. For a general free compound…

The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among different L\'evy processes: in the first model we…

Gaussian processes are rich distributions over functions, with generalization properties determined by a kernel function. When used for long-range extrapolation, predictions are particularly sensitive to the choice of kernel parameters. It…

We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to…

In this paper we study the existence of a unique solution for linear stochastic differential equations driven by a L\'evy process, where the initial condition and the coefficients are random and not necessarily adapted to the underlying…

This paper analyzes various classes of processes associated with the tempered positive Linnik (TPL) distribution. We provide several subordinated representations of TPL L\'evy processes and in particular establish a stochastic…

We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our G-normal-distribution in the sense that…

We construct intrinsic on-and off-diagonal upper and lower estimates for the transition probability density of a L\'evy process in small time. By intrinsic we mean that such estimates reflect the structure of the characteristic exponent of…

Levy flights and subdiffusive processes and their properties are discussed. We derive the space- and time-fractional transport equations, and consider their solutions in external potentials. An extensive list of references is included.

Standard GPs offer a flexible modelling tool for well-behaved processes. However, deviations from Gaussianity are expected to appear in real world datasets, with structural outliers and shocks routinely observed. In these cases GPs can fail…

In this paper, we first use PDE techniques and probabilistic methods to identify a kind of quasi-continuous random variables. Then we give a characterization of the $G$-integrable processes and get a kind of quasi-continuous processes by…

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…