Related papers: Elementary results on K processes with weights

This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of…

We discuss the Gamma Levy process, including path properties, the inverse process, integrability, and its spin-offs obtained by compounding, exponentiation, and other operations; further extendable to arbitrary sigma-finite continuous Borel…

In this paper, we consider a class of inhomogeneous semi-Markov processes directly based on intensity processes for marked point processes. We show that this class satisfies the semi-Markov properties defined elsewhere in the literature. We…

Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on…

We prove two basic structural properties of the algebraic $K$-theory of rings after $K(1)$-localization at an implicit prime $p$. Our first result (also recently obtained by Land--Meier--Tamme by different methods) states that $L_{K(1)}…

In this article is introduced and studied a set-indexed Markov property named C-Markov. This new definition fulfils one important expectation for a Markov property: there exists a natural set-indexed generalization of the concept of…

Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the…

In this work we show how to get advantage from the Riemann--Hilbert analysis in order to obtain first and second order differential equations for the orthogonal polynomials and associated functions with a weight on the unit circle. We…

Motivated by the study of the time evolution of random dynamical systems arising in a vast variety of domains --- ranging from physics to ecology ---, we establish conditions for the occurrence of a non-trivial asymptotic behaviour for…

Adaptive Markov chains are an important class of Monte Carlo methods for sampling from probability distributions. The time evolution of adaptive algorithms depends on past samples, and thus these algorithms are non-Markovian. Although there…

In this article we consider the Markovian products of invertible (not necessarily positive) matrices chosen from a strongly irreducible, contracting, finite set of matrices. We construct Markovian transfer operators and prove the spectral…

Let $r\ge k\ge 2$ be fixed positive integers. Let $\varrho_{r,k}$ denote the characteristic function of the set of $r$-tuples of positive integers with $k$-wise relatively prime components, that is any $k$ of them are relatively prime. We…

We prove the uniqueness of the martingale problem associated to some degenerate operators. The key point is to exploit the strong parallel between the new technique introduced by Bass and Perkins (From Probability to Geometry, vol. in honor…

The stochastic processes of finite length defined by recurrence relations request additional relations specifying the first terms of the process analogously to the initial conditions for the differential equations. As a general rule, in…

Irreversibility is commonly quantified by entropy production. An external observer can estimate it through measuring an observable that is antisymmetric under time-reversal like a current. We introduce a general framework that, inter alia,…

This article is a lecture note on the potential theory of (possibly non-reversible) Markov processes and on the connection of this theory with quantitative analysis of the metastability of stochastic processes.

The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…

Let R be a discrete valuation ring of unequal characteristic with fraction field K which contains a primitive p^2-th root of unity. Let X be a faithfully flat R-scheme and G be a finite abstract group. Let us consider a G-torsor Y_K\to X_K…

We study arithmetic properties of equivariant birational types introduced by Kontsevich, Pestun, and the second author.

The article presents mathematical generalization of results which originated as solutions of practical problems, in particular, the modeling of transitional processes in electrical circuits and problems of resource allocation. However, the…