Related papers: On $q$-scale functions of spectrally negative L\'e…
By using absolutely continuous lower bounds of the L\'evy measure, explicit gradient estimates are derived for the semigroup of the corresponding L\'evy process with a linear drift. A derivative formula is presented for the conditional…
We investigate the boundedness of ``vertical'' Littlewood--Paley--Stein square functions for the nonlocal fractional discrete Laplacian on the lattice $\mathbb{Z}$, where the underlying graphs are not locally finite. When $q\in[2,\infty)$,…
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…
Consider a class of functions of one real variable with the following uniqueness property: if a function f(x) from the class vanishes on a set of positive measure, then f is the zero function. In many instances, we would like to have a…
A L\'evy process is said to creep through a curve if, at its first passage time across this curve, the process reaches it with positive probability. We first study this property for bivariate subordinators. Given the graph…
This work is concerned with the dynamics of a class of slow-fast stochastic dynamical systems with non-Gaussian stable L\'evy noise with a scale parameter. Slow manifolds with exponentially tracking property are constructed, eliminating the…
Motion of particles in many systems exhibits a mixture between periods of random diffusive like events and ballistic like motion. In many cases, such systems exhibit strong anomalous diffusion, where low order moments $< |x(t)|^q >$ with…
Parabolic integro-differential model Cauchy problem is considered in the scale of Lp -spaces of functions whose regularity is defined by a scalable Levy measure. Existence and uniqueness of a solution is proved by deriving apriori…
The aim of this paper is to study the laws of the exponential functionals of the processes $X$ with independent increments, namely $$I_t= \int _0^t\exp(-X_s)ds, \,\, t\geq 0,$$ and also $$I_{\infty}= \int _0^{\infty}\exp(-X_s)ds.$$ Under…
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…
The reflected process of a random walk or L\'evy process arises in many areas of applied probability, and a question of particular interest is how the tail of the distribution of the heights of the excursions away from zero behaves…
We study the spectral properties of a highly occupied non-Abelian non-equilibrium plasma appearing ubiquitously in weak coupling descriptions of QCD matter. The spectral function of this far-from-equilibrium plasma is measured by employing…
We analyze Gaussian analytic functions (GAFs) defined as power series with coefficients modeled by discrete stationary Gaussian processes, utilizing their spectral measures. We revisit some limit theorems for random analytic functions and…
Stochastic treatments of magnetic resonance spectroscopy and optical spectroscopy require evaluations of functions like <exp(i int_0^t Q(s)ds)>, where t is time, Q(s) is the value of a stochastic process at time s, and the angular brackets…
We provide a L\'evy-It\^o decomposition of sample paths of L\'evy processes with values in complete locally convex Suslin spaces. This class of state spaces contains the well investigated examples of separable Banach spaces, as well as…
We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It works for any noise and segment level prior, e.g. Cauchy which can handle outliers.…
By using lower bound conditions of the L\'evy measure w.r.t. a nice reference measure, the coupling and strong Feller properties are investigated for the Markov semigroup associated with a class of linear SDEs driven by (non-cylindrical)…
Let $\{X_{1}(t)\}_{0\leq t\leq1}$ and $\{X_{2}(t)\}_{0\leq t\leq1}$ be two independent continuous centered Gaussian processes with covariance functions$R_{1}$ and $R_{2}$. This paper shows that if the covariance functions are of finite…
Various approaches to stochastic processes exist, noting that key properties such as measurability and continuity are not trivially satisfied. We introduce a new theory for Gaussian processes using improper linear functionals. Using a…
Consider on a manifold the solution $X$ of a stochastic differential equation driven by a L\'evy process without Brownian part. Sufficient conditions for the smoothness of the law of $X_t$ are given, with particular emphasis on noncompact…