Advances in Applied Probability

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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 paper i... 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 discounted penalty function at ruin is derived. This leads to a generalization of the defective renewal equations given by Willmot (1999) an... hiện toàn bộ
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 terms of the... 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 expected length of the shortest path between (0, 0) and (1, 0) in the Delaunay triangulation associated withXwhen the intensity ofXngoes to ∞. Simulations indicate that the correct value is about 1.04. We also prove that the expected len... 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 joint distri... 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 extended ... 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 introduced. A... hiện toàn bộ
The moments of the number of exits from a simply connected region
Advances in Applied Probability - Tập 30 Số 1 - Trang 167-180 - 1998
Robert Illsley
We generalise the work of Cramér and Leadbetter, Ylvisaker and Ito on the level crossings of a stationary Gaussian process to multivariate processes. Necessary and sufficient conditions for the existence of the expected number of crossingsE(C) of the boundary of a region of ℝpby a stationary vector stochastic process are obtained, along with an explicit formula forE(C) in the Gaussian case. A rigo... hiện toàn bộ
The intrinsic random functions and their applications
Advances in Applied Probability - Tập 5 Số 3 - Trang 439-468 - 1973
G. Matheron
The intrinsic random functions (IRF) are a particular case of the Guelfand generalized processes with stationary increments. They constitute a much wider class than the stationary RF, and are used in practical applications for representing non-stationary phenomena. The most important topics are: existence of a generalized covariance (GC) for which statistical inference is possible from a unique re... hiện toàn bộ
Single-server queues with impatient customers
Advances in Applied Probability - Tập 16 Số 4 - Trang 887-905 - 1984
François Baccelli, P. Boyer, G. Hébuterne
We consider a single-server queueing system in which a customer gives up whenever his waiting time is larger than a random threshold, his patience time. In the case of aGI/GI/1 queue with i.i.d. patience times, we establish the extensions of the classicalGI/GI/1 formulae concerning the stability condition and the relation between actual and virtual waiting-time distribution functions. We also prov... hiện toàn bộ
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