Related papers: Selfdecomposability, perpetuity and stopping times
Previous studies have used a specific success metric within an algorithmic search framework to prove machine learning impossibility results. However, this specific success metric prevents us from applying these results on other forms of…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging…
Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the dynamic variable. Nonlinearities in the scaling function of empirical moments…
The familiar cascade measures are sequences of random positive measures obtained on $[0,1]$ via $b$-adic independent cascades. To generalize them, this paper allows the random weights invoked in the cascades to take real or complex values.…
We study the probability densities of finite-time or \local Lyapunov exponents (LLEs) in low-dimensional chaotic systems. While the multifractal formalism describes how these densities behave in the asymptotic or long-time limit, there are…
An infinite convergent sum of independent and identically distributed random variables discounted by a multiplicative random walk is called perpetuity, because of a possible actuarial application. We give three disjoint groups of sufficient…
Bivariate partial-sums discrete probability distributions are defined. The question of the existence of a limit distribution for iterated partial summations is solved for finite-support bivariate distributions which satisfy conditions under…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
Inspired by many examples in nature, stochastic resetting of random processes has been studied extensively in the past decade. In particular, various models of stochastic particle motion were considered where upon resetting the particle is…
Levy walk at the finite velocity is considered. To analyze the spatial and temporal characteristics of this process, the method of moments has been used. The asymptotic distributions of the moments (at $t\to\infty$) have been obtained for…
In this article we introduce associative Look-Up Tables. With their help, pseudo sums are correctly determined. The set of limit distributions in a pseudo-summation scheme of i.i.d. random variables is described. Also, two special cases…
The initial conditions of our universe appear to us in the form of a classical probability distribution that we probe with cosmological observations. In the current leading paradigm, this probability distribution arises from a quantum…
We consider a L\'evy process $Y(t)$ that is not permanently observed, but rather inspected at Poisson($\omega$) moments only, over an exponentially distributed time $T_\beta$ with parameter $\beta$. The focus lies on the analysis of the…
This article focuses on properties of monotone convolutions. A criterion for infinite divisibility and time evolution of convolution semigroups are mainly studied. In particular, we clarify that many analogues of the classical results of…
We consider the general branching random walk under minimal assumptions, which in particular guarantee that the empirical particle distribution admits an almost sure central limit theorem. For such a process, we study the large time decay…
An important line of research is the investigation of the laws of random variables known as Dirichlet means as discussed in Cifarelli and Regazzini(1990). However there is not much information on inter-relationships between different…
In the paper, multivariate probability distributions are considered that are representable as scale mixtures of multivariate elliptically contoured stable distributions. It is demonstrated that these distributions form a special subclass of…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
We completely characterize $\Delta$- and local subexponentialities of positive-half compound Poisson distributions and extend the characterization on two-sided distributions. Moreover, $\Delta$-subexponentiality of infinitely divisible…