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作者：Crudu, A.; Debussche, A.; Muller, A.; Radulescu, O.
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; Universite de Montpellier
摘要：We study the asymptotic behavior of multiscale stochastic gene networks using weak limits of Markov jump processes. Depending on the time and concentration scales of the system, we distinguish four types of limits: continuous piecewise deterministic processes (PDP) with switching, PDP with jumps in the continuous variables, averaged PDP, and PDP with singular switching. We justify rigorously the convergence for the four types of limits. The convergence results can be used to simplify the stoch...
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作者：Bassetti, Federico; Ladelli, Lucia
作者单位：University of Pavia; Polytechnic University of Milan
摘要：This paper deals with a class of Boltzmann equations on the real line, extensions of the well-known Kac caricature. A distinguishing feature of the corresponding equations is that therein, the collision gain operators are defined by N-linear smoothing transformations. These kind of problems have been studied, from an essentially analytic viewpoint, in a recent paper by Bobylev, Cercignani and Gamba [Comm. Math. Phys. 291 (2009) 599-644]. Instead, the present work rests exclusively on probabili...
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作者：Benaim, Michel; Faure, Mathieu
作者单位：University of Neuchatel
摘要：This paper considers a stochastic approximation algorithm, with decreasing step size and martingale difference noise. Under very mild assumptions, we prove the nonconvergence of this process toward a certain class of repulsive sets for the associated ordinary differential equation (ODE). We then use this result to derive the convergence of the process when the ODE is cooperative in the sense of Hirsch [SIAM J. Math. Anal. 16 (1985) 423-439]. In particular, this allows us to extend significantl...
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作者：Johnstone, Iain M.; Ma, Zongming
作者单位：Stanford University; University of Pennsylvania
摘要：We study the rate of convergence for the largest eigenvalue distributions in the Gaussian unitary and orthogonal ensembles to their Tracy-Widom limits. We show that one can achieve an O(N-2/3.) rate with particular choices of the centering and scaling constants. The arguments here also shed light on more complicated cases of Laguerre and Jacobi ensembles, in both unitary and orthogonal versions. Numerical work shows that the suggested constants yield reasonable approximations, even for surpris...
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作者：Biggins, J. D.
作者单位：University of Sheffield
摘要：This paper gives conditions for the rightmost particle in the nth generation of a multitype branching random walk to have a speed, in the sense that its location divided by n converges to a constant as n goes to infinity. Furthermore, a formula for the speed is obtained in terms of the reproduction laws. The case where the collection of types is irreducible was treated long ago. In addition, the asymptotic behavior of the number in the nth generation to the right of na is obtained. The initial...
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作者：Pfaffelhuber, P.; Staab, P. R.; Wakolbinger, A.
作者单位：University of Freiburg; Goethe University Frankfurt
摘要：We consider an infinite-dimensional system of stochastic differential equations describing the evolution of type frequencies in a large population. The type of an individual is the number of deleterious mutations it carries, where fitness of individuals carrying k mutations is decreased by alpha k for some alpha > 0. Along the individual lines of descent, new mutations accumulate at rate lambda per generation, and each of these mutations has a probability gamma per generation to disappear. Whi...
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作者：Bender, Christian
作者单位：Saarland University
摘要：We characterize absence of arbitrage with simple trading strategies in a discounted market with a constant bond and several risky assets. We show that if there is a simple arbitrage, then there is a 0-admissible one or an obvious one, that is, a simple arbitrage which promises a minimal riskless gain of E, if the investor trades at all. For continuous stock models, we provide an equivalent condition for absence of 0-admissible simple arbitrage in terms of a property of the fine structure of th...
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作者：Kersting, Goetz
作者单位：Goethe University Frankfurt
摘要：We derive the asymptotic distribution of the total length L-n of a Beta(2 - alpha, alpha)-coalescent tree for 1 < alpha < 2, starting from n individuals. There are two regimes: If alpha 1/2(1 + root 5), then L-n suitably resealed has a stable limit distribution of index alpha. Otherwise L-n just has to be shifted by a constant (depending on n) to get convergence to a nondegenerate limit distribution. As a consequence, we obtain the limit distribution of the number S-n of segregation sites. The...
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作者：Broutin, Nicolas; Holmgren, Cecilia
作者单位：University of Cambridge
摘要：We consider the model of random trees introduced by Devroye [SIAM J. Comput. 28 (1999) 409-432]. The model encompasses many important randomized algorithms and data structures. The pieces of data (items) are stored in a randomized fashion in the nodes of a tree. The total path length (sum of depths of the items) is a natural measure of the efficiency of the algorithm/data structure. Using renewal theory, we prove convergence in distribution of the total path length toward a distribution charac...
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作者：Janson, Svante; Luczak, Tomasz; Turova, Tatyana; Vallier, Thomas
作者单位：Uppsala University; Adam Mickiewicz University; Lund University; University of Helsinki
摘要：Bootstrap percolation on the random graph C-n,C-p is a process of spread of activation on a given realization of the graph with a given number of initially active nodes. At each step those vertices which have not been active but have at least r >= 2 active neighbors become active as well. We study the size A* of the final active set. The parameters of the model are, besides r (fixed) and n (tending to infinity), the size a = a(n) of the initially active set and the probability p = p(n) of the ...
