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作者：Ma, Ruibo; Durrett, Rick
作者单位：Duke University
摘要：We study an evolutionary game in which a producer at x gives birth at rate 1 to an offspring sent to a randomly chosen point in x + N-c, while a cheater at x gives birth at rate lambda > 1 times the fraction of producers in x + N-d and sends its offspring to a randomly chosen point in x + N-c. We first study this game on the d-dimensional torus (Z mod L)(d) with N-d = (Z mod L)(d) and N-c = the 2d nearest neighbors. If we let L -> infinity then t -> infinity the fraction of producers converges...
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作者：Rodosthenous, Neofytos; Zhang, Hongzhong
作者单位：University of London; Queen Mary University London; Columbia University
摘要：We study the optimal stopping of an American call option in a random time-horizon under exponential spectrally negative Levy models. The random time-horizon is modeled as the so-called Omega default clock in insurance, which is the first time when the occupation time of the underlying Levy process below a level y, exceeds an independent exponential random variable with mean 1/q > 0. We show that the shape of the value function varies qualitatively with different values of q and y. In particula...
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作者：Chatterjee, Shirshendu; Zeitouni, Ofer
作者单位：City University of New York (CUNY) System; City College of New York (CUNY); Weizmann Institute of Science; New York University
摘要：We consider the searching for a trail in a maze composite hypothesis testing problem, in which one attempts to detect an anomalous directed path in a lattice 2D box of side n based on observations on the nodes of the box. Under the signal hypothesis, one observes independent Gaussian variables of unit variance at all nodes, with zero mean off the anomalous path and mean mu(n) on it. Under the null hypothesis, one observes i.i.d. standard Gaussians on all nodes. Arias-Castro et al. [Ann. Statis...
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作者：Foondun, Mohammud; Joseph, Mathew; Li, Shiu-Tang
作者单位：University of Strathclyde; University of Sheffield; Utah System of Higher Education; University of Utah
摘要：We show that a large class of stochastic heat equations can be approximated by systems of interacting stochastic differential equations. As a consequence, we prove various comparison principles extending earlier works of [Stoch. Stoch. Rep. 37 (1991) 225-245] and [Ann. Probab. 45 (2017) 377403] among others. Among other things, our results enable us to obtain sharp estimates on the moments of the solution. A main technical ingredient of our method is a local limit theorem which is of independe...
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作者：Gulikers, Lennart; Lelarge, Marc; Massoulie, Laurent
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Universite PSL; Ecole Normale Superieure (ENS)
摘要：We consider the Degree-Corrected Stochastic Block Model (DC-SBM): a random graph on n nodes, having i.i.d. weights (phi u)(u)(n)=i (possibly heavytailed), partitioned into q >= 2 asymptotically equal-sized clusters. The model parameters are two constants a, b > 0 and the finite second moment of the weights Phi((2)). Vertices u and v are connected by an edge with probability phi u phi v/na when they are in the same class and with probability phi u phi v/nb otherwise. We prove that it is informa...
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作者：Mueller, Marvin S.
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Moving boundary problems allow to model systems with phase transition at an inner boundary. Motivated by problems in economics and finance, we set up a price-time continuous model for the limit order book and consider a stochastic and nonlinear extension of the classical Stefan-problem in one space dimension. Here, the paths of the moving interface might have unbounded variation, which introduces additional challenges in the analysis. Working on the distribution space, the Ito-Wentzell formula...
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作者：Bernardin, Cedric; Goncalves, Patricia; Jara, Milton
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Universidade de Lisboa
摘要：We consider a chain of weakly harmonic coupled oscillators perturbed by a conservative noise. We show that by tuning accordingly the coupling constant, energy can diffuse like a Brownian motion or superdiffuse like a maximally 3/2-stable asymmetric Levy process. For a critical value of the coupling, the energy diffusion is described by a family of Levy processes which interpolate between these two processes.
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作者：Swart, Jan M.
作者单位：Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences
摘要：In 1964, G. J. Stigler introduced a stochastic model for the evolution of an order book on a stock market. This model was independently rediscovered and generalized by H. Luckock in 2003. In his formulation, traders place buy and sell limit orders of unit size according to independent Poisson processes with possibly different intensities. Newly arriving buy (sell) orders are either immediately matched to the best available matching sell (buy) order or stay in the order book until a matching or...
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作者：Thacker, Debleena; Volkov, Stanislav
作者单位：Lund University
摘要：Start with a graph with a subset of vertices called the border. A particle released from the origin performs a random walk on the graph until it comes to the immediate neighbourhood of the border, at which point it joins this subset thus increasing the border by one point. Then a new particle is released from the origin and the process repeats until the origin becomes a part of the border itself. We are interested in the total number xi of particles to be released by this final moment. We show...
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作者：Biskup, Marek; Procaccia, Eviatar B.
作者单位：University of California System; University of California Los Angeles; Charles University Prague; Texas A&M University System; Texas A&M University College Station
摘要：We study paths of time-length t of a continuous-time random walk on Z(2) subject to self-interaction that depends on the geometry of the walk range and a collection of random, uniformly positive and finite edge weights. The interaction enters through a Gibbs weight at inverse temperature beta; the energy is the total sum of the edge weights for edges on the outer boundary of the range. For edge weights sampled from a translation-invariant, ergodic law, we prove that the range boundary condensa...
