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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 ...
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作者：Amei, Amei; Sawyer, Stanley
作者单位：Nevada System of Higher Education (NSHE); University of Nevada Las Vegas; Washington University (WUSTL)
摘要：We derive a Poisson random field model for population site polymorphisms differences within and between two species that share a relatively recent common ancestor. The model can be either equilibrium or time inhomogeneous. We first consider a random field of Markov chains that describes the fate of a set of individual mutations. This field is approximated by a Poisson random field from which we can make inferences about the amounts of mutation and selection that have occurred in the history of...
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作者：Ichiba, Tomoyuki; Karatzas, Ioannis
作者单位：University of California System; University of California Santa Barbara
摘要：We examine the behavior of n Brownian particles diffusing on the real line with bounded, measurable drift and bounded, piecewise continuous diffusion coefficients that depend on the current configuration of particles. Sufficient conditions are established for the absence and for the presence of triple collisions among the particles. As an application to the Atlas model for equity markets, we study a special construction of such systems of diffusing particles using Brownian motions with reflect...
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作者：Atchade, Yves F.
作者单位：University of Michigan System; University of Michigan
摘要：There is a growing interest in the literature for adaptive Markov chain Monte Carlo methods based on sequences of random transition kernels {P-n} where the kernel P-n is allowed to have an invariant distribution pi(n) not necessarily equal to the distribution of interest pi (target distribution). These algorithms are designed such that as n -> infinity, P-n converges to P. a kernel that has the correct invariant distribution pi. Typically, P is a kernel with good convergence properties, but on...
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作者：Pang, Guodong; Whitt, Ward
作者单位：Columbia University
摘要：We establish continuity of the integral representation y(t) = x(t) + integral(t)(0)h(y(s)) ds, t >= 0, mapping a function x into a function y when the underlying function space D is endowed with the Skorohod M-1 topology. We apply this integral representation with the continuous mapping theorem to establish heavy-traffic stochastic-process limits for many-server queueing models when the limit process has jumps unmatched in the converging processes as can occur with bursty arrival processes or ...
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作者：Bacry, Emmanuel; Gloter, Arnaud; Hoffmann, Marc; Muzy, Jean Francois
作者单位：Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Institut Polytechnique de Paris; ENSAE Paris; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Engineering & Systems Sciences (INSIS)
摘要：Multifractal analysis of multiplicative random cascades is revisited within the framework of mixed asymptotics. In this new framework, the observed process can be modeled by a concatenation of independent binary cascades and statistics are estimated over a sample whose size increases as the resolution scale (or the sampling period) becomes finer. This allows one to continuously interpolate between the situation where one studies a single cascade sample at arbitrary fine scales and where, at fi...
