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作者：Kyprianou, A. E.; Pardo, J. C.; Rivero, V.
作者单位：University of Bath
摘要：Understanding the space time features of how a Levy process crosses a constant barrier for the first time, and indeed the last time, is a problem which is central to many models in applied probability such as queueing theory, financial and actuarial mathematics, optimal stopping problems, the theory of branching processes, to name but a few. In Doney and Kyprianou [Ann. Appl. Probab. 16 (2006) 91-106] a new quintuple law was established for a general Levy process at first passage below a fixed...
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作者：Kuznetsov, Alexey
作者单位：York University - Canada
摘要：In this paper we introduce a ten-parameter family of Levy processes for which we obtain Wiener-Hopf factors and distribution of the supremum process in semi-explicit form. This family allows an arbitrary behavior of small jumps and includes processes similar to the generalized tempered stable, KoBoL and CGMY processes. Analytically it is characterized by the property that the characteristic exponent is a meromorphic function, expressed in terms of beta and digamma functions. We prove that the ...
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作者：Barral, Julien; Jin, Xiong; Mandelbrot, Benoit
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris 13; Inria; Yale University
摘要：The familiar cascade measures are sequences of random positive measures obtained on [0, 1] via b-adic independent cascades. To generalize them, this paper allows the random weights invoked in the cascades to take real or complex values. This yields sequences of random functions whose possible strong or weak limits are natural candidates for modeling multifractal phenomena. Their asymptotic behavior is investigated, yielding a sufficient condition for almost sure uniform convergence to nontrivi...
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作者：Hitczenko, Pawel; Wesolowski, Jacek
作者单位：Drexel University; Warsaw University of Technology
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作者：Ethier, S. N.; Lee, Jiyeon
作者单位：Utah System of Higher Education; University of Utah; Yeungnam University
摘要：The antique Mills Futurity slot machine has two unusual features. First, if a player loses 10 times in a row, the 10 lost coins are returned. Second, the payout distribution varies from coup to coup in a manner that is nonrandom and periodic with period 10. It follows that the machine is driven by a 100-state irreducible period-10 Markov chain. Here, we evaluate the stationary distribution of the Markov chain, and this leads to a strong law of large numbers and a central limit theorem for the ...
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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...
