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作者：Fort, Jean-Claude; Pages, Gilles
作者单位：Universite de Lorraine; Sorbonne Universite
摘要：Some existence and stability results for the equilibrium points of the one-dimensional Kohonen self-organizing neural network with two neighbors are extended to most nonincreasing neighborhood functions. All the functions mentioned in the neural literature are included. The assumption on the stimuli distribution is weakened, too. In the multidimensional setting, we derive from a general formula various stability and instability results.
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作者：Meyn, Sean P.
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：This paper treats transience for queueing network models by considering an associated fluid limit model. If starting from any initial condition the fluid limit model explodes at a linear rate, then the associated queueing network with i.i.d. service times and a renewal arrival process explodes faster than any fractional power.
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作者：Barsky, David J.; Gandolfi, Alberto
作者单位：California State University System; California State University San Marcos; University of Rome Tor Vergata
摘要：In this paper we present an asymptotic estimator, obtained by observing a noisy image, for the parameters of both a stationary Markov random field and an independent Bernoulli noise. We first estimate the parameter of the noise by solving a polynomial equation of moderate degree (about 6-7 in the one-dimensional Ising model and about 10-15 in the two-dimensional Ising model, for instance) and then apply the maximum pseudo-likelihood method after removing the noise. Our method requires no extra...
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作者：Biggins, J. D.
作者单位：University of Sheffield
摘要：A general (Crump-Mode-Jagers) spatial branching process is considered. The asymptotic behavior of the numbers present at time t in sets of the form [ta, infinity) is obtained. As a consequence it is shown that if B-t is the position of the rightmost person at time t, B-t/t converges to a constant, which can be obtained from the individual reproduction law, almost surely on the survival set of the process. This generalizes the known discrete-time results.
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作者：Wormald, Nicholas C.
作者单位：University of Melbourne
摘要：General criteria are given to ensure that in a family of discrete random processes, given parameters exhibit convergence to the solution of a system of differential equations. As one application we consider random graph processes in which the maximum degree is bounded and show that the numbers of vertices of given degree exhibit this convergence as the total number of vertices tends to infinity. Two other applications are to random processes which generate independent sets of vertices in rando...
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作者：Kotelenez, Peter
作者单位：University System of Ohio; Case Western Reserve University
摘要：The Navier-Stokes equation for the vorticity of a viscous and incompressible fluid in R-2 is analyzed as a macroscopic equation for an underlying microscopic model of randomly moving vortices. We consider N point vortices whose positions satisfy a stochastic ordinary differential equation on R-2N, where the fluctuation forces are state dependent and driven by Brownian sheets. The state dependence is modeled to yield a short correlation length e between the fluctuation forces of different vorti...
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作者：Asmussen, Soren; Glynn, Peter; Pitman, Jim
作者单位：Aalborg University; Stanford University; University of California System; University of California Berkeley
摘要：This paper is concerned with various aspects of the simulation of one-dimensional reflected (or regulated) Brownian motion. The main result shows that the discretization error associated with the Euler scheme for simulation of such a process has both a strong and weak order of convergence of precisely 1/2. This contrasts with the faster order 1 achievable for simulations of SDE's without reflecting boundaries. The asymptotic distribution of the discretization error is described using Williams'...
