Related papers: Random Time Change and Related Evolution Equations…
In this article densities (and their derivatives) of subordinators and inverse subordinators are considered. Under minor restrictions, generally milder than the existing in the literature, using a useful modification of the saddle point…
We prove large time asymptotics for solutions of the KP I equation with small initial data. Our assumptions on the initial data rule out lump solutions but give a precise description of the radiation field at large times. Our analysis uses…
Lying between traditional parabolic and hyperbolic equations, time-fractional wave equations of order $\alpha\in(1,2)$ in time inherit both decaying and oscillating properties. In this article, we establish a long-time asymptotic estimate…
In this paper, we present the asymptotic properties of the moment estimator for autoregressive (AR for short) models subject to Markovian changes in regime under the assumption that the errors are uncorrelated but not necessarily…
The non-exponential relaxation is shown to result from subordination by inverse tempered \alpha-stable processes. The main feature of tempered \alpha-stable processes is a finiteness of their moments, and the class of random processes…
We consider the discrete-time migration-recombination equation, a deterministic, nonlinear dynamical system that describes the evolution of the genetic type distribution of a population evolving under migration and recombination in a law of…
Open quantum walks often lead to a classical asymptotic behavior. Here, we look for a simple open quantum walk whose asymptotic behavior can be non-classical. We consider a discrete-time quantum walk on n-cycle subject to a random…
We develop asymptotic approximations that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and related settings. In batched adaptive settings where the decision at one stage can affect…
We consider hyperbolic equations with time-dependent coefficients and develop an abstract framework to derive the asymptotic behaviour of the representation of solutions for large times. We are dealing with generic situations where the…
We study properties of a piecewise deterministic Markov process modeling the changes in concentration of specific antibodies. The evolution of densities of the process is described by a stochastic semigroup. The long-time behaviour of this…
The asymptotic variance is an important criterion to evaluate the performance of Markov chains, especially for the central limit theorems. We give the variational formulas for the asymptotic variance of discrete-time (non-reversible) Markov…
In this paper, we consider the large time asymptotic behavior of solutions to systems of two cubic nonlinear Klein-Gordon equations in one space dimension. We classify the systems by studying the quotient set of a suitable subset of systems…
The growth-fragmentation equation models systems of particles that grow and split as time proceeds. An important question concerns the large time asymptotic of its solutions. Doumic and Escobedo ($2016$) observed that when growth is a…
In this paper we explore the theory of fractional powers of non-negative (and not necessarily self-adjoint) operators and its amazing relationship with the Chebyshev polynomials of the second kind to obtain results of existence, regularity…
Inspired by the works of \cite{baz2} and \cite{kian}, this study develops an abstract framework for analyzing differential equations with space-dependent fractional time derivatives and bounded operators. Within this framework, we establish…
We establish a generic method to analyze the time evolution of open quantum many-body systems. Our approach is based on a variational integration of the quantum master equation describing the dynamics and naturally connects to a variational…
We develop the idea of non-Markovian CTRW (continuous time random walk) approximation to the evolution of interacting particle systems, which leads to a general class of fractional kinetic measure-valued evolutions with variable order. We…
The continuous time random walk model has been widely applied in various fields, including physics, biology, chemistry, finance, social phenomena, etc. In this work, we present an algorithm that utilizes a subordinate formula to generate…
In this paper we study the convergence to fractional Brownian motion for long memory time series having independent innovations with infinite second moment. For the sake of applications we derive the self-normalized version of this theorem.…
In this paper we consider a new mathematical extension of the Black-Scholes model in which the stochastic time and stock share price evolution is described by two independent random processes. The parent process is Brownian, and the…