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作者：Chen, Zhen-Qing; Fan, Wai-Tong (Louis)
作者单位：University of Washington; University of Washington Seattle; University of Wisconsin System; University of Wisconsin Madison
摘要：A new non-conservative stochastic reaction diffusion system in which two families of random walks in two adjacent domains interact near the interface is introduced and studied in this paper. Such a system can be used to model the transport of positive and negative charges in a solar cell or the population dynamics of two segregated species under competition. We show that in the macroscopic limit, the particle densities converge to the solution of a coupled nonlinear heat equations. For this, w...
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作者：Helmes, Kurt L.; Stockbridge, Richard H.; Zhu, Chao
作者单位：Humboldt University of Berlin; University of Wisconsin System; University of Wisconsin Milwaukee
摘要：This paper establishes conditions for optimality of an (s, S) ordering policy for the minimization of the long-term average cost of one-dimensional diffusion inventory models. The class of such models under consideration have general drift and diffusion coefficients and boundary points that are consistent with the notion that demand should tend to reduce the inventory level. Characterization of the cost of a general (s, S) policy as a function F of two variables naturally leads to a nonlinear ...
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作者：Bovier, Anton; Hartung, Lisa
作者单位：University of Bonn; New York University; University of Bonn
摘要：We extend the results of Arguin et al. [Probab. Theory Related Fields 157 (2013) 535-574] and Aidekon et al. [Probab. Theory Related Fields 157 (2013) 405-451] on the convergence of the extremal process of branching Brownian motion by adding an extra dimension that encodes the location of the particle in the underlying Galton-Watson tree. We show that the limit is a cluster point process on R+ x R where each cluster is the atom of a Poisson point process on R+ x R with a random intensity measu...
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作者：Bayraktar, Erhan; Ya, Song
作者单位：University of Michigan System; University of Michigan; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
摘要：We analyze a robust version of the Dynkin game over a set P of mutually singular probabilities. We first prove that conservative player's lower and upper value coincide (let us denote the value by V). Such a result connects' the robust Dynkin game with second-order doubly reflected backward stochastic differential equations. Also, we show that the value process V is a submartingale under an appropriately defined nonlinear expectation E up to the first time tau* when V meets the lower payoff pr...
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作者：Jenkins, Paul A.; Spano, Dario
作者单位：University of Warwick; University of Warwick
摘要：The Wright-Fisher family of diffusion processes is a widely used class of evolutionary models. However, simulation is difficult because there is no known closed-form formula for its transition function. In this article, we demonstrate that it is in fact possible to simulate exactly from a broad class of Wright-Fisher diffusion processes and their bridges. For those diffusions corresponding to reversible, neutral evolution, our key idea is to exploit an eigenfunction expansion of the transition...
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作者：He, Yukun; Knowles, Antti
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove that the linear statistics of the eigenvalues of a Wigner matrix converge to a universal Gaussian process on all mesoscopic spectral scales, that is, scales larger than the typical eigenvalue spacing and smaller than the global extent of the spectrum.
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作者：Amir, Gideon; Angel, Omer; Kozma, Gady
作者单位：Bar Ilan University; University of British Columbia; Weizmann Institute of Science
摘要：We examine diffusion-limited aggregation for a one-dimensional random walk with long jumps. We achieve upper and lower bounds on the growth rate of the aggregate as a function of the number of moments a single step of the walk has. In this paper, we handle the case of transient walks.
