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作者：Molchanov, S. A.; Surgailis, D.; Woyczynski, W. A.
作者单位：University of North Carolina; University of North Carolina Charlotte; Vilnius University; University System of Ohio; Case Western Reserve University; University System of Ohio; Case Western Reserve University
摘要：Burgers turbulence is an accepted formalism for the adhesion model of the large-scale distribution of matter in the universe. The paper uses variational methods to establish evolution of quasi-Voronoi (curved boundaries) tessellation structure of shock fronts for solutions of the inviscid nonhomogeneous Burgers equation in R-d in the presence of random forcing due to a degenerate potential. The mean rate of growth of the quasi-Voronoi cells is calculated and a scaled limit random tessellation ...
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作者：Rothmann, Mark D.; Russo, Ralph P.
作者单位：University System of Georgia; Georgia Institute of Technology; University of Iowa
摘要：Consider a system into which units having random magnitude enter at arbitrary times and remain active (present in the system) for random periods. Suppose units of high magnitude have stochastically greater lifetimes ffi tend to stay active for longer periods. than units of low magnitude. Of interest is the process {mu(t): t >= 0}, where mu(t) denotes the average magnitude of all units active at time t. We give conditions which guarantee the convergence of mu(t) and we determine the form of the...
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作者：Roberts, G. O.; Gelman, A.; Gilks, W. R.
作者单位：University of Cambridge; Columbia University; University of Cambridge; MRC Biostatistics Unit
摘要：This paper considers the problem of scaling the proposal distribution of a multidimensional random walk Metropolis algorithm in order to maximize the efficiency of the algorithm. The main result is a weak convergence result as the dimension of a sequence of target densities, n, converges to infinity. When the proposal variance is appropriately scaled according to n, the sequence of stochastic processes formed by the first component of each Markov chain converges to the appropriate limiting Lan...
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作者：Bertoin, Jean
作者单位：Sorbonne Universite
摘要：Consider a completely asymmetric Levy process which has absolutely continuous transition probabilities. We determine the exponential decay parameter rho and the quasistationary distribution for the transition probabilities of the evy process killed as it exits from a finite interval, prove that the killed process is rho-positive and specify the rho-invariant function and measure.
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作者：O'Neill, Philip
作者单位：University of Bradford
摘要：This paper is concerned with a model for the spread of an epidemic in a closed, homogeneously mixed population in which new infections occur at rate beta(z)xy/(x+y), where x, y and z denote, respectively, the numbers of susceptible, infective and removed individuals. Thus the infection mechanism depends upon the number of removals to date, reflecting behavior change in response to the progress of the epidemic. For a deterministic version of the model, a recurrent solution is obtained when beta...
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作者：Bean, N. G.; Bright, L.; Latouche, G.; Pearce, C. E. M.; Pollett, P. K.; Taylor, P. G.
作者单位：University of Adelaide; Universite Libre de Bruxelles; University of Queensland
摘要：For evanescent Markov processes with a single transient communicating class, it is often of interest to examine the limiting probabilities that the process resides in the various transient states, conditional on absorption not having taken place. Such distributions are known as quasi-stationary (or limiting-conditional) distributions. In this paper we consider the determination of the quasi-stationary distribution of a general level-independent quasi-birth-and-death process (QBD). This distrib...
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作者：Carmona, Rene A.; Xu, Lin
作者单位：Princeton University
摘要：We consider the diffusive scaling limit for the transport of a passive scalar in a two-dimensional time-dependent incompressible Gaussian velocity field and in the presence of molecular diffusivity. We prove that homogenization holds in this limiting regime and we derive some simple properties of the effective diffusivity tensor.
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作者：Komorowski, Tomasz; Papanicolaou, George
作者单位：Michigan State University; Stanford University
摘要：We prove that the solution of a system of random ordinary differential equations dX(t)/dt = V(t, X(t) with diffusive scaling, X-epsilon(t) = epsilon X(t/epsilon(2)), converges weakly to a Brownian motion when epsilon down arrow 0. We assume that V(t,X), t is an element of R, X is an element of R-d is a d-dimensional, random, incompressible, stationary Gaussian field which has mean zero and decorrelates in finite time.
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作者：Schmidli, H.
作者单位：Aarhus University
摘要：In applied probability one is often interested in the asymptotic behavior of a certain quantity. If a regenerative phenomenon can be imbedded, then one has the problem that the event of interest may have occurred but cannot be observed at the renewal points. In this paper an extension to the renewal theorem is proved which shows that the quantity of interest converges. As an illustration an open problem in risk theory is solved.
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作者：Rucinski, A.; Wormald, N. C.
作者单位：Adam Mickiewicz University; University of Melbourne
摘要：Suppose that a process begins with n isolated vertices, to which edges are added randomly one by one so that the maximum degree of the induced graph is always at most 2. In a previous article, the authors showed that as n -> infinity, with probability tending to 1, the result of this process is a graph with n edges. The number of l-cycles in this graph is shown to be asymptotically Poisson (l >= 3), and other aspects of this random graph model are studied.
