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作者：Kelly, David
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：In this article, we consider diffusion approximations for a general class of stochastic recursions. Such recursions arise as models for population growth, genetics, financial securities, multiplicative time series, numerical schemes and MCMC algorithms. We make no particular probabilistic assumptions on the type of noise appearing in these recursions. Thus, our technique is well suited to recursions where the noise sequence is not a semi-martingale, even though the limiting noise may be. Our m...
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作者：Delattre, Sylvain; Fournier, Nicolas; Hoffmann, Marc
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; Universite PSL; Universite Paris-Dauphine
摘要：We generalise the construction of multivariate Hawkes processes to a possibly infinite network of counting processes on a directed graph G. The process is constructed as the solution to a system of Poisson driven stochastic differential equations, for which we prove pathwise existence and uniqueness under some reasonable conditions. We next investigate how to approximate a standard N-dimensional Hawkes process by a simple inhomogeneous Poisson process in the mean field framework where each pai...
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作者：Cantarella, Jason; Shonkwiler, Clayton
作者单位：University System of Georgia; University of Georgia; Colorado State University System; Colorado State University Fort Collins
摘要：A closed equilateral random walk in 3-space is a selection of unit length vectors giving the steps of the walk conditioned on the assumption that the sum of the vectors is zero. The sample space of such walks with n edges is the (2n- 3)-dimensional Riemannian manifold of equilateral closed polygons in R-3. We study closed random walks using the symplectic geometry of the (2n - 6)-dimensional quotient of the manifold of polygons by the action of the rotation group SO(3). The basic objects of st...
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作者：Ortmann, Janosch; Quastel, Jeremy; Remenik, Daniel
作者单位：University of Toronto; Universidad de Chile; Universidad de Chile
摘要：We obtain exact formulas for moments and generating functions of the height function of the asymmetric simple exclusion process at one spatial point, starting from special initial data in which every positive even site is initially occupied. These complement earlier formulas of E. Lee [J. Stat. Phys. 140 (2010) 635-647] but, unlike those formulas, ours are suitable in principle for asymptotics. We also explain how our formulas are related to divergent series formulas for half-flat KPZ of Le Do...
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作者：Gimbert, Hugo; Renault, Jerome; Sorin, Sylvain; Venel, Xavier; Zielonka, Wieslaw
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Bordeaux; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Sorbonne Universite; Universite Paris Cite; heSam Universite; Universite Pantheon-Sorbonne; Universite Paris Cite
摘要：We study the existence of different notions of value in two-person zero sum repeated games where the state evolves and players receive signals. We provide some examples showing that the limsup value (and the uniform value) may not exist in general. Then we show the existence of the value for any Borel payoff function if the players observe a public signal including the actions played. We also prove two other positive results without assumptions on the signaling structure: the existence of the ...
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作者：Anantharam, Venkat; Salez, Justin
作者单位：University of California System; University of California Berkeley; Universite Paris Cite
摘要：We determine the asymptotic behavior of the maximum subgraph density of large random graphs with a prescribed degree sequence. The result applies in particular to the Erdos-Renyi model, where it settles a conjecture of Hajek [IEEE Trans. Inform. Theory 36 (1990) 1398-1414]. Our proof consists in extending the notion of balanced loads from finite graphs to their local weak limits, using unimodularity. This is a new illustration of the objective method described by Aldous and Steele [In Probabil...
