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作者：Yu, Feng; Etheridge, Alison; Cuthbertson, Charles
作者单位：University of Bristol; University of Oxford; Morgan Stanley
摘要：We consider the accumulation of beneficial and deleterious mutations in large asexual populations. The rate of adaptation is affected by the total mutation rate, proportion of beneficial mutations and population size N. We show that regardless of mutation rates, as long as the proportion of beneficial mutations is strictly positive, the adaptation rate is at least O(log(1-delta) N) where delta can be any small positive number, if the population size is sufficiently large. This shows that if th...
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作者：Bramson, Maury; Dai, J. G.; Harrison, J. M.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University System of Georgia; Georgia Institute of Technology; Stanford University
摘要：Consider a semimartingale reflecting Brownian motion (SRBM) Z whose state space is the d-dimensional nonnegative orthant. 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 that specifies the boundary behavior of Z. We say that Z is positive recurrent, or stable, if the expected time to hit an arbitrary open neighborhood of the origin is finite for every starting state. In dimension d = 2, necessary and sufficient ...
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作者：Ding, Xue; Jiang, Tiefeng
作者单位：Jilin University; University of Minnesota System; University of Minnesota Twin Cities
摘要：In this paper, we investigate the spectral properties of the adjacency and the Laplacian matrices of random graphs. We prove that: (i) the law of large numbers for the spectral norms and the largest eigenvalues of the adjacency and the Laplacian matrices; (ii) under some further independent conditions, the normalized largest eigenvalues of the Laplacian matrices are dense in a compact interval almost surely; (iii) the empirical distributions of the eigenvalues of the Laplacian matrices converg...
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作者：Mertikopoulos, Panayotis; Moustakas, Aris L.
作者单位：National & Kapodistrian University of Athens
摘要：We study repeated games where players use an exponential learning scheme in order to adapt to an ever-changing environment. If the game's payoffs are subject to random perturbations, this scheme leads to a new stochastic version of the replicator dynamics that is quite different from the aggregate shocks approach of evolutionary game theory. Irrespective of the perturbations' magnitude, we find that strategies which are dominated (even iteratively) eventually become extinct and that the game's...
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作者：Dembo, Amir; Montanari, Andrea
作者单位：Stanford University; Stanford University; Stanford University
摘要：We consider ferromagnetic Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the cavity prediction for the limiting free energy per spin is correct for any positive temperature and external field. Further, local marginals can be approximated by iterating a set of mean field (cavity) equations. Both results are achieved by proving the local convergence of the Bol...
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作者：Bertoin, Jean
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：We consider a spatial branching process with emigration in which children either remain at the same site as their parents or migrate to new locations and then found their own colonies. We are interested in asymptotics of the partition of the total population into colonies for large populations with rare migrations. Under appropriate regimes, we establish weak convergence of the rescaled partition to some random measure that is constructed from the restriction of a Poisson point measure to a ce...
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作者：Fernholz, Daniel; Karatzas, Ioannis
作者单位：University of Texas System; University of Texas Austin
摘要：In a Markovian model for a financial market, we characterize the best arbitrage with respect to the market portfolio that can be achieved using nonanticipative investment strategies, in terms of the smallest positive solution to a parabolic partial differential inequality; this is determined entirely on the basis of the covariance structure of the model. The solution is intimately related to properties of strict local martingales and is used to generate the investment strategy which realizes t...
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作者：Jacod, Jean; Todorov, Viktor
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite; Northwestern University
摘要：We consider a process X(t), which is observed on a finite time interval [0, T], at discrete times 0, Delta(n), 2 Delta(n), ... . This process is an Ito semimartingale with stochastic volatility sigma(2)(t). Assuming that X has jumps on [0, T], we derive tests to decide whether the volatility process has jumps occurring simultaneously with the jumps of X(t). There are two different families of tests for the two possible null hypotheses (common jumps or disjoint jumps). They have a prescribed as...
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作者：Alexander, Kenneth S.; Zygouras, Nikos
作者单位：University of Southern California; University of Warwick
摘要：We consider a polymer with configuration modelled by the trajectory of a Markov chain, interacting with a potential of form u + V-n when it visits a particular state 0 at time n, with {V-n} representing i.i.d. quenched disorder. There is a critical value of u above which the polymer is pinned by the potential. A particular case not covered in a number of previous studies is that of loop exponent one, in which the probability of an excursion of length n takes the form phi(n)/n for some slowly v...
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作者：Elskens, Yves; Pardoux, Etienne
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：The one-dimensional motion of any number N of particles in the field of many independent waves (with strong spatial correlation) is formulated as a second-order system of stochastic differential equations, driven by two Wiener processes. In the limit of vanishing particle mass m -> 0, or, equivalently, of large noise intensity, we show that the momenta of all N particles converge weakly to N independent Brownian motions, and this convergence holds even if the noise is periodic. This justifies ...
