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作者：Barbato, David; Flandoli, Franco; Morandin, Francesco
作者单位：University of Padua; University of Pisa; University of Parma
摘要：A stochastic version of an inviscid dyadic model of turbulence, with multiplicative noise, is proved to exhibit energy dissipation in spite of the formal energy conservation. As a consequence, global regular solutions cannot exist. After some reductions, the main tool is the escape bahavior at infinity of a certain birth and death process.
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作者：Brightwell, Graham; Luczak, Malwina
作者单位：University of London; London School Economics & Political Science
摘要：A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring together two different classes of random processes. In one class, we are given a fixed causal set, and we consider random natural extensions of this causal set: we think of the random enumeration as being generated one point at a time. In the other class of proces...
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作者：De Marco, Stefano
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Scuola Normale Superiore di Pisa
摘要：We study smoothness of densities for the solutions of SDEs whose coefficients are smooth and nondegenerate only on an open domain D. We prove that a smooth density exists on D and give upper bounds for this density. Under some additional conditions (mainly dealing with the growth of the coefficients and their derivatives), we formulate upper bounds that are suitable to obtain asymptotic estimates of the density for large values of the state variable (tail estimates). These results specify and ...
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作者：Daskalakis, Constantinos; Dimakis, Alexandros G.; Mossel, Elchanan
作者单位：Massachusetts Institute of Technology (MIT); University of Southern California; University of California System; University of California Berkeley
摘要：We study how the structure of the interaction graph of a game affects the existence of pure Nash equilibria. In particular, for a fixed interaction graph, we are interested in whether there are pure Nash equilibria arising when random utility tables are assigned to the players. We provide conditions for the structure of the graph under which equilibria are likely to exist and complementary conditions which make the existence of equilibria highly unlikely. Our results have immediate implication...
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作者：Olvera-Cravioto, Mariana; Blanchet, Jose; Glynn, Peter
作者单位：Columbia University; Stanford University
摘要：Two of the most popular approximations for the distribution of the steady-state waiting time, W-infinity, of the M/G/1 queue are the so-called heavy-traffic approximation and heavy-tailed asymptotic, respectively. If the traffic intensity, rho, is close to 1 and the processing times have finite variance, the heavy-traffic approximation states that the distribution of W-infinity is roughly exponential at scale O((1 - rho)(-1)), while the heavy tailed asymptotic describes power law decay in the ...
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作者：Anderson, David F.; Ganguly, Arnab; Kurtz, Thomas G.
作者单位：University of Wisconsin System; University of Wisconsin Madison; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We perform an error analysis for numerical approximation methods of continuous time Markov chain models commonly found in the chemistry and biochemistry literature. The motivation for the analysis is to be able to compare the accuracy of different approximation methods and, specifically, Euler tau-leaping and midpoint tau-leaping. We perform our analysis under a scaling in which the size of the time discretization is inversely proportional to some (bounded) power of the norm of the state of th...
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作者：Bhamidi, Shankar; Bresler, Guy; Sly, Allan
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of California System; University of California Berkeley; Microsoft
摘要：A variety of random graph models has been developed in recent years to study a range of problems on networks, driven by the wide availability of data from many social, telecommunication, biochemical and other networks. A key model, extensively used in sociology literature, is the exponential random graph model. This model seeks to incorporate in random graphs the notion of reciprocity, that is, the larger than expected number of triangles and other small subgraphs. Sampling from these distribu...
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作者：Oreshkin, Boris N.; Coates, Mark J.
作者单位：McGill University
摘要：This paper examines the impact of approximation steps that become necessary when particle filters are implemented on resource-constrained platforms. We consider particle filters that perform intermittent approximation, either by subsampling the particles or by generating a parametric approximation. For such algorithms, we derive time-uniform bounds on the weak-sense L-p error and present associated exponential inequalities. We motivate the theoretical analysis by considering the leader node pa...
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作者：Kanoria, Yashodhan; Montanari, Andrea
作者单位：Stanford University; Stanford University
摘要：A voter sits on each vertex of an infinite tree of degree k, and has to decide between two alternative opinions. At each time step, each voter switches to the opinion of the majority of her neighbors. We analyze this majority process when opinions are initialized to independent and identically distributed random variables. In particular, we bound the threshold value of the initial bias such that the process converges to consensus. In order to prove an upper bound, we characterize the process o...
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作者：Bramson, Maury
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Semimartingale reflecting Brownian motions (SRBMs) are diffusion processes with state space the d-dimensional nonnegative orthant, in the interior of which the processes evolve according to a Brownian motion, and that reflect against the boundary in a specified manner. The data for such a process are a drift vector theta, a nonsingular d x d covariance matrix Sigma, and a d x d reflection matrix R. A standard problem is to determine under what conditions the process is positive recurrent. Nece...
