Related papers: Non-commutative L\'evy processes for generalized (…
A basic diagnostic of entanglement in mixed quantum states is known as the partial transpose and the corresponding entanglement measure is called the logarithmic negativity. Despite the great success of logarithmic negativity in…
Given $n$ equidistant realisations of a L\'evy process $(L_t,\,t\ge 0)$, a natural estimator $\hat N_n$ for the distribution function $N$ of the L\'evy measure is constructed. Under a polynomial decay restriction on the characteristic…
The aim of this paper is to establish a global asymptotic equivalence between the experiments generated by the discrete (high frequency) or continuous observation of a path of a L{\'e}vy process and a Gaussian white noise experiment…
We review some recent developments in white noise analysis and quantum probability. We pay a special attention to spaces of test and generalized functionals of some L\'evy white noises, as well as as to the structure of quantum white noise…
In this paper, we investigate the stochastic counterpart of the generalized Wright analysis introduced in Beghin et al.~ in Integral Equations and Operator Theory, {\bf 97}, 2025. We define a new class of non-Gaussian and non-Markovian…
Our first result concerns a characterisation by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalised version of Mecke's formula. En passant, it also allows to…
As an analogue to the explicit formula in the stable case, the asymptotic behavior at the origin of the renormalized zero resolvent of one-dimensional L\'evy processes is studied under certain regular variation conditions on the…
The main purpose of this chapter is to present some theoretical aspects of parametric estimation of L\'evy processes based on high-frequency sampling, with a focus on infinite activity pure-jump models. Asymptotics for several classes of…
In this paper we establish a multivariable non-commutative generalization of L\"owner's classical theorem from 1934 characterizing operator monotone functions as real functions admitting analytic continuation mapping the upper complex…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…
We propose isomorphism type identities for nonlinear functionals of general infinitely divisible processes. Such identities can be viewed as an analogy of the Cameron-Martin formula for Poissonian infinitely divisible processes but with…
In the present work, we establish the approximation of nonlinear stochastic partial differential equation (SPDE) driven by cylindrical {\alpha}-stable L\'evy processes via modulation or amplitude equations. We study SPDEs with a cubic…
A standard approach to analysis of noise-induced effects in stochastic dynamics assumes a Gaussian character of the noise term describing interaction of the analyzed system with its complex surroundings. An additional assumption about the…
In this paper an analytic operator-valued generalized Feynman integral was studied on a very general Wiener space $C_{a,b}[0,T]$. The general Wiener space $C_{a,b}[0,T]$ is a function space which is induced by the generalized Brownian…
Given a basis for a polynomial ring, the coefficients in the expansion of a product of some of its elements in terms of this basis are called linearization coefficients. These coefficients have combinatorial significance for many classical…
A fundamental result of Biane (1998) states that a process with freely independent increments has the Markov property, but that there are two kinds of free Levy processes: the first kind has stationary increments, while the second kind has…
The fundamentals of Statistical Mechanics require a fresh definition in the context of the developments in Classical Mechanics of integrable and chaotic systems. This is done with the introduction of Micro Partitions ; a union of disjoint…
We construct the number operator for particles obeying infinite statistics, defined by a generalized q-deformation of the Heisenberg algebra, and prove the positivity of the norm of linearly independent state vectors.
Complex dynamical systems which are governed by anomalous diffusion often can be described by Langevin equations driven by L\'evy stable noise. In this article we generalize nonlinear stochastic differential equations driven by Gaussian…