Related papers: Functional central limit theorems for Markov-modul…
In the present paper the infinite-server MMAPkGk queueing model with random resource vector of customers, marked MAP arrival and semi-Markov (SM) arrival of catastrophes is considered. The joint generating functions (PGF) of transient and…
We study the effect of investor inertia on stock price fluctuations with a market microstructure model comprising many small investors who are inactive most of the time. It turns out that semi-Markov processes are tailor made for modelling…
In [20], the authors addressed the question of the averaging of a slow-fast Piecewise Deterministic Markov Process (PDMP) in infinite dimension. In the present paper, we carry on and complete this work by the mathematical analysis of the…
Through the analysis of a dataset of ultra high frequency order book updates, we introduce a model which accommodates the empirical properties of the full order book together with the stylized facts of lower frequency financial data. To do…
We obtain necessary and sufficient conditions for the regular variation of the variance of partial sums of functionals of discrete and continuous-time stationary Markov processes with normal transition operators. We also construct a class…
Queueing networks are notoriously difficult to analyze sans both Markovian and stationarity assumptions. Much of the theoretical contribution towards performance analysis of time-inhomogeneous single class queueing networks has focused on…
We consider a two-node tandem queueing network in which the upstream queue is GI/GI/1 and each job reuses its upstream service requirement when moving to the downstream queue. Both servers employ the first-in-first-out policy. To…
We establish heavy traffic limit theorems for queue-length processes in critically loaded single class queueing networks with state dependent arrival and service rates. A distinguishing feature of our model is non-Markovian state…
We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete…
In this paper we examine the asymptotic theory for U-statistics and V-statistics of discontinuous Ito semimartingales that are observed at high frequency. For different types of kernel functions we show laws of large numbers and associated…
We investigate the convergence in distribution of sequential empirical processes of dependent data indexed by a class of functions F. Our technique is suitable for processes that satisfy a multiple mixing condition on a space of functions…
We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service…
The standard small-time functional central limit theorem of semimartingales has been established in (Gerhold, S., Kleinert, M., Porkert, P., and Shkolnikov, M. (2015). Small time central limit theorems for semimartingales with applications.…
Consider an N-dimensional Markov chain obtained from N one-dimensional random walks by Doob h-transform with the q-Vandermonde determinant. We prove that as N becomes large, these Markov chains converge to an infinite-dimensional Feller…
This paper considers a BMAP/M/$\infty$ queue with a batch Markovian arrival process (BMAP) and an exponential service time distribution. We first prove that the BMAP/M/$\infty$ queue is stable if and only if the expectation of the logarithm…
The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes, especially stochastic integrals and differential equations. In this paper, general central limit theorems and functional…
We consider a branching system consisting of particles moving according to a Markov family in $\Rd$ and undergoing subcritical branching with a constant rate $V>0$. New particles immigrate to the system according to homogeneous space-time…
We study fluctuations of mean-field interacting particle systems around their McKean--Vlasov limit. Our main result provides a uniform-in-time quantitative central limit theorem for the fluctuation process, with convergence rate of order…
We study a Markov random process describing a muscle molecular motor behavior. Every motor is either bound up with a thin filament or unbound. In the bound state the motor creates a force proportional to its displacement from the neutral…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…