Related papers: The Levy-Ito Decomposition theorem
L\'evy processes on bialgebras are families of infinitely divisible representations. We classify the generators of L\'evy processes on the compact forms of the quantum algebras $U_q(g)$, where $g$ is a simple Lie algebra. Then we show how…
We show the existence of L\'evy-type stochastic processes in one space dimension with characteristic triplets that are either discontinuous at thresholds, or are stable-like with stability index functions for which the closures of 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…
L\'evy's Upward Theorem says that the conditional expectation of an integrable random variable converges with probability one to its true value with increasing information. In this paper, we use methods from effective probability theory to…
Within a path integral formalism for non-Gaussian price fluctuations we set up a simple stochastic calculus and derive a natural martingale for option pricing from the wealth balance of options, stocks, and bonds. The resulting formula is…
Let $T$ be an arbitrary operator bounded from $L^{p_0}(w)$ into $L^{p_0, \infty}(w)$ for every weight $w$ in the Muckenhoupt class $A_{p_0}$. It is proved in this article that the distribution function of $Tf$ with respect to any weight $u$…
Analogue to the well-known Langevin Monte Carlo method, in this article we provide a method to sample from a target distribution \(\pi\) by simulating a solution of a stochastic differential equation. Hereby, the stochastic differential…
It is shown that some convolution semigroups of infinitely divisible measures are invariant under the random integral mappings $I^{h,r}_{(a,b]}$ defined in $(\star)$ below. The converse implication is specified for the semigroups of…
The objects under investigation are the stochastic integrals with respect to free Levy processes. We define such integrals for square-integrable integrands, as well as for a certain general class of bounded integrands. Using the product…
We summarize the relations among three classes of laws: infinitely divisible, selfdecomposable and stable. First we look at them as the solutions of the Central Limit Problem; then their role is scrutinized in relation to the Levy and the…
We use the theory of fully matricial, or non-commutative, functions to investigate infinite divisibility and limit theorems in operator-valued non-commutative probability. Our main result is an operator-valued analogue of the Bercovici-Pata…
Using the theory of free random variables (FRV) and the Coulomb gas analogy, we construct stable random matrix ensembles that are random matrix generalizations of the classical one-dimensional stable L\'{e}vy distributions. We show that the…
After reviewing a large body of literature on the modeling of bivariate discrete distributions with finite support, \cite{Gee20} made a compelling case for the use of $I$-projections in the sense of \cite{Csi75} as a sound way to attempt to…
In 1972, J. S. Lew established a reasonable conjecture regarding an axiomatic characterization for the one-dimensional Riemann-Liouville integral. This conjecture was proved by Cartwright and McMullen in 1978. After that, little further…
In 1980 M{\'e}tivier characterized the analytic (and Gevrey) hypoellipticity of $L^2$-solvable partial linear differential operators by a-priori estimates. In this note we extend this characterization to ultradifferentiable hypoellipticity…
We introduce G-L\'{e}vy processes which develop the theory of processes with independent and stationary increments under the framework of sublinear expectations. We then obtain the L\'{e}vy-Khintchine formula and the existence for…
This note provides additional interpretation for the counterfactual outcome distribution and corresponding unconditional quantile "effects" defined and estimated by Firpo, Fortin, and Lemieux (2009) and Chernozhukov, Fern\'andez-Val, and…
We consider a class of assets whose risk-neutral pricing dynamics are described by an exponential L\'evy-type process subject to default. The class of processes we consider features locally-dependent drift, diffusion and default-intensity…
It is shown that every Leavitt path algebra L of an arbitrary directed graph E over a field K is an arithmetical ring, that is, the two-sided ideals of L form a distributive lattice. It is also shown that L is a multiplication ring, that…
This paper gives a complete characterization of infinitely divisible semimartingales, i.e., semimartingales whose finite dimensional distributions are infinitely divisible. An explicit and essentially unique decomposition of such…