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作者：Bertacchi, D.; Lanchier, N.; Zucca, F.
作者单位：University of Milano-Bicocca; Arizona State University; Arizona State University-Tempe; Polytechnic University of Milan
摘要：We introduce spatially explicit stochastic processes to model multispecies host-symbiont interactions. The host environment is static, modeled by the infinite percolation cluster of site percolation. Symbionts evolve on the infinite cluster through contact or voter type interactions, where each host may be infected by a colony of symbionts. In the presence of a single symbiont species, the condition for invasion as a function of the density of the habitat of hosts and the maximal size of the c...
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作者：Appuhamillage, Thilanka; Bokil, Vrushali; Thomann, Enrique; Waymire, Edward; Wood, Brian
作者单位：Oregon State University; Oregon State University
摘要：Advective skew dispersion is a natural Markov process defined by a diffusion with drift across an interface of jump discontinuity in a piecewise constant diffusion coefficient. In the absence of drift, this process may be represented as a function of alpha-skew Brownian motion for a uniquely determined value of alpha = alpha*; see Ramirez et al. [Multiscale Model. Simul. 5 (2006) 786-801]. In the present paper, the analysis is extended to the case of nonzero drift. A determination of the (join...
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作者：Nakashima, Makoto
作者单位：Kyoto University
摘要：We consider the branching random walks in d-dimensional integer lattice with time-space i.i.d. offspring distributions. Then the normalization of the total population is a nonnegative martingale and it almost surely converges to a certain random variable. When d >= 3 and the fluctuation of environment satisfies a certain uniform square integrability then it is nondegenerate and we prove a central limit theorem for the density of the population in terms of almost sure convergence.
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作者：Fukasawa, Masaaki
作者单位：Japan Science & Technology Agency (JST); University of Osaka
摘要：Limit distributions for the error in approximations of stochastic integrals by Riemann sums with stochastic partitions are studied. The integrands and integrators are supposed to be one-dimensional continuous semimartingales. Lower bounds for asymptotic conditional variance of the error are given and effective discretization schemes which attain the bounds are explicitly constructed. Two examples of their applications are given; efficient delta hedging strategies under fixed or linear transact...
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作者：Bansaye, Vincent; Delmas, Jean-Francois; Marsalle, Laurence; Tran, Viet Chi
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite de Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We study the evolution of a particle system whose genealogy is given by a supercritical continuous time Galton-Watson tree. The particles move independently according to a Markov process and when a branching event occurs, the offspring locations depend on the position of the mother and the number of offspring. We prove a law of large numbers for the empirical measure of individuals alive at time t. This relies on a probabilistic interpretation of its intensity by mean of an auxiliary process. ...
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作者：Chan, Hock Peng; Lai, Tze Leung
作者单位：National University of Singapore; Stanford University
摘要：Sequential Monte Carlo methods which involve sequential importance sampling and resampling are shown to provide a versatile approach to computing probabilities of rare events. By making use of martingale representations of the sequential Monte Carlo estimators, we show how resampling weights can be chosen to yield logarithmically efficient Monte Carlo estimates of large deviation probabilities for multidimensional Markov random walks.
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作者：Appuhamillage, Thilanka; Bokil, Vrushali; Thomann, Enrique; Waymire, Edward; Wood, Brian
作者单位：Oregon State University; Oregon State University
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作者：Assaf, Sami; Diaconis, Persi; Soundararajan, K.
作者单位：Massachusetts Institute of Technology (MIT); Stanford University; Stanford University
摘要：We study how many riffle shuffles are required to mix n cards if only certain features of the deck are of interest, for example, suits disregarded or only the colors of interest. For these features the number of shuffles drops from 3/2 log(2) n to log(2) n. We derive closed formulae and an asymptotic rule of thumb formula which is remarkably accurate.
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作者：Chatterjee, Sourav; Diaconis, Persi; Sly, Allan
作者单位：New York University; Stanford University; Microsoft
摘要：Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have graph limits in the sense of Lovasz and Szegedy with identifiable limits. This allows simple determination of other features such as the number of triangles. The argument proceeds by studying a natural exponential model having the degree sequence as a suffici...
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作者：Dereich, Steffen
作者单位：Philipps University Marburg
摘要：We introduce and analyze multilevel Monte Carlo algorithms for the, computation of E(f) (Y), where Y = (Y(t))t is an element of[0, 1] is the solution of a multidimensional Levy-driven stochastic differential equation and f is a real-valued function on the path space. The algorithm relies on approximations obtained by simulating large jumps of the Levy process individually and applying a Gaussian approximation for the small jump part. Upper bounds are provided for the worst case error over the ...
