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作者：Kuznetsov, A.; Kyprianou, A. E.; Pardo, J. C.; van Schaik, K.
作者单位：York University - Canada; University of Bath; CIMAT - Centro de Investigacion en Matematicas
摘要：We develop a completely new and straightforward method for simulating the joint law of the position and running maximum at a fixed time of a general Levy process with a view to application in insurance and financial mathematics. Although different, our method takes lessons from Carr's so-called Canadization technique as well as Doney's method of stochastic bounds for Levy processes; see Carr [Rev. Fin. Studies 11 (1998) 597-626] and Doney [Ann. Probab. 32 (2004) 1545-1552]. We rely fundamental...
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作者：Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：We derive the joint density of market weights, at fixed times and suitable stopping times, of the volatility-stabilized market models introduced by Fernholz and Karatzas in [Ann. Finan. 1 (2005) 149-177]. The argument rests on computing the exit density of a collection of independent Bessel-square processes of possibly different dimensions from the unit simplex. We show that the law of the market weights is the same as that of the multi-allele Wright-Fisher diffusion model, well known in popul...
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作者：Chauvin, Brigitte; Pouyanne, Nicolas; Sahnoun, Reda
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider a two-color Polya urn in the case when a fixed number S of balls is added at each step. Assume it is a large urn that is, the second eigenvalue m of the replacement matrix satisfies 1/2 < m/S <= 1. After n drawings, the composition vector has asymptotically a first deterministic term of order n and a second random term of order n(m/S). The object of interest is the limit distribution of this random term. The method consists in embedding the discrete-time urn in continuous time, get...
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作者：Graham, Benjamin; Grimmett, Geoffrey
作者单位：University of British Columbia; Universite PSL; Ecole Normale Superieure (ENS); University of Cambridge
摘要：A sharp-threshold theorem is proved for box-crossing probabilities on the square lattice. The models in question are the random-cluster model near the self-dual point p(sd)(q) = root q/(1 + root q), the Ising model with external field, and the colored random-cluster model. The principal technique is an extension of the influence theorem for monotonic probability measures applied to increasing events with no assumption of symmetry.
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作者：Berestycki, J.; Harris, S. C.; Kyprianou, A. E.
作者单位：Sorbonne Universite; Universite Paris Cite; University of Bath
摘要：We formulate the notion of the classical Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) reaction diffusion equation associated with a homogeneous conservative fragmentation process and study its traveling waves. Specifically, we establish existence, uniqueness and asymptotics. In the spirit of classical works such as McKean [Comm. Pure Appl. Math. 28 (1975) 323-331] and [Comm. Pure Appl. Math. 29 (1976) 553-554], Neveu [In Seminar on Stochastic Processes (1988) 223-242 Birkh user] and Chauvin [...
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作者：Bramson, Maury
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Join the shortest queue (JSQ) refers to networks whose incoming jobs are assigned to the shortest queue from among a randomly chosen subset of the queues in the system. After completion of service at the queue, a job leaves the network. We show that, for all nonidling service disciplines and for general interarrival and service time distributions, such networks are stable when they are subcritical. We then obtain uniform bounds on the tails of the marginal distributions of the equilibria for f...
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作者：Todorov, Viktor; Tauchen, George
作者单位：Northwestern University; Duke University
摘要：This paper derives the asymptotic behavior of realized power variation of pure-jump Ito semimartingales as the sampling frequency within a fixed interval increases to infinity. We prove convergence in probability and an associated central limit theorem for the realized power variation as a function of its power. We apply the limit theorems to propose an efficient adaptive estimator for the activity of discretely-sampled Ito semimartingale over a fixed interval.
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作者：Betz, Volker; Ueltschi, Daniel; Velenik, Yvan
作者单位：University of Warwick; University of Geneva
摘要：We study the distribution of cycle lengths in models of nonuniform random permutations with cycle weights. We identify several regimes. Depending on the weights, the length of typical cycles grows like the total number n of elements, or a fraction of n or a logarithmic power of n.
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作者：Bai, Z. D.; Liu, H. X.; Wong, W. K.
作者单位：Northeast Normal University - China; Northeast Normal University - China; National University of Singapore; Hong Kong Baptist University
摘要：Let S(n) = 1/nX(n)X*(n) where X(n) = {X(ij)} is a p x n matrix with i.i.d. complex standardized entries having finite fourth moments. Let Y(n)(t(1), t(2), sigma) = root p(x(n)(t(1))*(S(n) + sigma I)(-1)x(n)(t(2)) - x(n)(t(1))*x(n)(t(2)) m(n)(sigma)) in which sigma > 0 and m(n)(sigma) = integral dF(yn)(x)/x+sigma where F(yn)(x) is the Marcenko-Pastur law with parameter y(n) = p/n; which converges to a positive constant as n -> infinity, and x(n)(t(1)) and x(n)(t(2)) are unit vectors in C(p), ha...
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作者：Kuna, Tobias; Lebowitz, Joel L.; Speer, Eugene R.
作者单位：University of Reading; Rutgers University System; Rutgers University New Brunswick
摘要：We give necessary and sufficient conditions for a pair of (generalized) functions rho(1)(r(1)) and rho(2) (r(1), r(2)), r(i) is an element of X, to be the density and pair correlations of some point process in a topological space X, for example, R(d), Z(d) or a subset of these. This is an infinite-dimensional version of the classical truncated moment problem. Standard techniques apply in the case in which there can be only a bounded number of points in any compact subset of X. Without this res...
