Advances in Applied Probability

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Fractional diffusion and fractional heat equation
Advances in Applied Probability - Tập 32 Số 4 - Trang 1077-1099 - 2000
J. M. Angulo, M. D. Ruiz‐Medina, Vo Anh, Wilfried Grecksch
This paper introduces a fractional heat equation, where the diffusion operator is the composition of the Bessel and Riesz potentials. Sharp bounds are obtained for the variance of the spatial and temporal increments of the solution. These bounds establish the degree of singularity of the sample paths of the solution. In the case of unbounded spatial domain, a solution is formulated in term...... hiện toàn bộ
Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes
Advances in Applied Probability - Tập 25 Số 3 - Trang 518-548 - 1993
Sean Meyn, Richard L. Tweedie
In Part I we developed stability concepts for discrete chains, together with Foster–Lyapunov criteria for them to hold. Part II was devoted to developing related stability concepts for continuous-time processes. In this paper we develop criteria for these forms of stability for continuous-parameter Markovian processes on general state spaces, based on Foster-Lyapunov inequalities for the e...... hiện toàn bộ
Transient behavior of regulated Brownian motion, I: Starting at the origin
Advances in Applied Probability - Tập 19 Số 3 - Trang 560-598 - 1987
Joseph Abate, Ward Whitt
A natural model for stochastic flow systems is regulated or reflecting Brownian motion (RBM), which is Brownian motion on the positive real line with constant negative drift and constant diffusion coefficient, modified by an impenetrable reflecting barrier at the origin. As a basis for understanding how stochastic flow systems approach steady state, this paper provides relatively simple de...... hiện toàn bộ
Multiple channel queues in heavy traffic. I
Advances in Applied Probability - Tập 2 Số 1 - Trang 150-177 - 1970
Donald L. Iglehart, Ward Whitt
The queueing systems considered in this paper consist ofrindependent arrival channels andsindependent service channels, where as usual the arrival and service channels are independent. Arriving customers form a single queue and are served in the order of their arrival without defections. We shall treat two distinct modes of operation fo...... hiện toàn bộ
Hitting-time and occupation-time bounds implied by drift analysis with applications
Advances in Applied Probability - Tập 14 Số 3 - Trang 502-525 - 1982
Bruce Hajek
Bounds of exponential type are derived for the first-hitting time and occupation times of a real-valued random sequence which has a uniform negative drift whenever the sequence is above a fixed level. The only other assumption on the random sequence is that the increments satisfy a uniform exponential decay condition. The bounds provide a flexible technique for proving stability of process...... hiện toàn bộ
Criteria for classifying general Markov chains
Advances in Applied Probability - Tập 8 Số 4 - Trang 737-771 - 1976
Richard L. Tweedie
The aim of this paper is to present a comprehensive set of criteria for classifying as recurrent, transient, null or positive the sets visited by a general state space Markov chain. When the chain is irreducible in some sense, these then provide criteria for classifying the chain itself, provided the sets considered actually reflect the status of the chain as a whole. The first part of the...... hiện toàn bộ
On a general class of renewal risk process: analysis of the Gerber-Shiu function
Advances in Applied Probability - Tập 37 Số 3 - Trang 836-856 - 2005
Shuanming Li, José Garrido
We consider a compound renewal (Sparre Andersen) risk process with interclaim times that have a Kn distribution (i.e. the Laplace transform of their density function is a ratio of two polynomials of degree at most n ∈ N). The Laplace transform of the expected discoun...... hiện toàn bộ
Stretch factor in a planar Poisson–Delaunay triangulation with a large intensity
Advances in Applied Probability - Tập 50 Số 01 - Trang 35-56 - 2018
Nicolas Chenavier, Olivier Devillers
AbstractLetX:=Xn∪ {(0, 0), (1, 0)}, whereXnis a planar Poisson point process of intensityn. We provide a first nontrivial lower bound for the distance between the ...... hiện toàn bộ
Characterization of the Generalized Pólya Process and its Applications
Advances in Applied Probability - Tập 46 Số 04 - Trang 1148-1171 - 2014
Ji Hwan
In this paper some important properties of the generalized Pólya process are derived and their applications are discussed. The generalized Pólya process is defined based on the stochastic intensity. By interpreting the defined stochastic intensity of the generalized Pólya process, the restarting property of the process is discussed. Based on the restarting property of the process, the join...... hiện toàn bộ
A single-server queue with server vacations and a class of non-renewal arrival processes
Advances in Applied Probability - Tập 22 Số 3 - Trang 676-705 - 1990
David M. Lucantoni, K.S. Meier-Hellstern, Marcel F. Neuts
We study a single-server queue in which the server takes a vacation whenever the system becomes empty. The service and vacation times and the arrival process are all assumed to be mutually independent. The successive service times and the vacation times each form independent, identically distributed sequences with general distributions. A new class of non-renewal arrival processes is intro...... hiện toàn bộ
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