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作者：Kouritzin, MA; Long, HW
作者单位：University of Alberta
摘要：In the context of simulating the transport of a chemical or bacterial contaminant through a moving sheet of water, we extend a well-established method of approximating reaction-diffusion equations with Markov chains by allowing convection, certain Poisson measure driving sources and a larger class of reaction functions. Our alterations also feature dramatically slower Markov chain state change rates often yielding a ten to one-hundredfold simulation speed increase over the previous version of ...
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作者：Gromoll, HC; Puha, AL; Williams, RJ
作者单位：California State University System; California State University San Marcos; University of California System; University of California San Diego
摘要：Consider a single server queue with renewal arrivals and i.i.d. service times in which the server operates under a processor sharing service discipline. To describe the evolution of this system, we use a measure valued process that keeps track of the residual service times of all jobs in the system at any given time. From this measure valued process, one can recover the traditional performance processes, including queue length and workload. We propose and study a critical fluid model (or forma...
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作者：Baldi, P; Caramellino, L
作者单位：University of Rome Tor Vergata
摘要：We consider a general one-dimensional diffusion process and we study the probability of crossing a boundary for the associated pinned diffusion as the time at which the conditioning takes place goes to zero. We provide asymptotics for this probability as well as a first order development. We consider also the cases of two boundaries possibly depending on the time. We give applications to simulation.
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作者：Budhiraja, A
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：The classical results on the ergodic properties of the nonlinear filter previously have been proved under the crucial assumption that the signal process and the observation noise are independent. This assumption is quite restrictive and many important problems in engineering and stochastic control correspond to filtering models with correlated signal and noise. Unlike the case of independent signal and noise, the filter process in the general correlated case may not be Markov even if the signa...
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作者：Schmidli, H
作者单位：University of Copenhagen
摘要：We consider a classical risk model and allow investment into a risky asset modelled as a Black-Scholes model as well as (proportional) reinsurance. Via the Hamilton-Jacobi-Bellman approach we find a candidate for the optimal strategy and develop a numerical procedure to solve the HJB equation. We prove a verification theorem in order to show that any increasing solution to the HJB equation is bounded and solves the optimisation problem. We prove that an increasing solution to the HJB equation ...
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作者：Marchand, R
作者单位：Universite de Lorraine
摘要：In this work we are interested in the variations of the asymptotic shape in first passage percolation on Z(2) according to the passage time distribution. Our main theorem extends a result proved by van den Berg and Kesten, which says that the time constant strictly decreases when the distribution of the passage time is modified in a certain manner (according to a convex order extending stochastic comparison). Van den Berg and Kesten's result requires, when the minimum r of the support of the p...
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作者：Dantzer, JF; Robert, P
作者单位：Universite Paris Saclay
摘要：The stability properties of the bandwidth allocation algorithm first fit are analyzed for the distributions concentrated on three sizes for the requests. We give the explicit expression of the ergodicity condition of this model; it involves a quadratic functional of the input parameters. The stochastic processes describing these systems are string valued Markov processes. The notion of a smooth random state is introduced. Starting from a smooth random state the fluid limits of the process can ...
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作者：Assaf, D; Goldstein, L; Samuel-Cahn, E
作者单位：Hebrew University of Jerusalem; University of Southern California
摘要：Let X-i be nonnegative, independent random variables with finite expectation, and X-n* = max{X-1, ..., X-n}. The value EXn* is what can be obtained by a prophet. A mortal on the other hand, may use k greater than or equal to I stopping rules t(1), ..., t(k), yielding a return of E[max(i=1), ..., k X-ti]. For n greater than or equal to k the optimal return is V-k(n) (X-1, ..., X-n) = sup E[max(i=1) ,..., k X-ti] where the supremum is over all stopping rules t(1), ..., t(k) such that P(t(i) less...
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作者：Comets, F; Fernández, R; Ferrari, PA
作者单位：Universite Paris Cite; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); Universidade de Sao Paulo
摘要：We present a perfect simulation algorithm for stationary processes indexed by Z, with summable memory decay. Depending on the decay, we construct the process on finite or semi-infinite intervals, explicitly from an i.i.d. uniform sequence. Even though the process has infinite memory, its value at time 0 depends only on a finite, but random, number of these uniform variables. The algorithm is based on a recent regenerative construction of these measures by Ferrari, Maass, Martinez and Ney. As a...
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作者：Jordan, J
作者单位：University of Oxford
摘要：We consider a class of probabilistic models obtained by iterating random functions of k random variables. We prove an analogue of the weak law of large numbers and under a symmetry condition we prove a strong law. The symmetry condition is satisfied if the initial random variables are exchangeable. Our results can be used to give stronger results than those previously obtained in the special case where the function is deterministic. Both types of models have applications in physics and in comp...
