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作者：Touzi, N
作者单位：Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris
摘要：We study the stochastic control problem of maximizing expected utility from terminal wealth, when the wealth process is subject to shocks produced by a general marked point process; the problem of the agent is to derive the optimal allocation of his wealth between investments in a nonrisky asset and in a (costly) insurance strategy which allows lowering the level of the shocks. The agent's optimization problem is related to a suitable dual stochastic control problem in which the constraint on ...
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作者：Baryshnikov, YM; Gnedin, AV
作者单位：Eindhoven University of Technology; University of Gottingen
摘要：Let random points X-1,...,X-n be sampled in strict sequence from a continuous product distribution on Euclidean d-space. At the time X-j is observed it must be accepted or rejected. The subsequence of accepted points must increase in each coordinate. We show that the maximum expected length of a subsequence selected is asymptotic to gamman(1/(d+1)) and give the exact value of gamma. This extends the root 2n result by Samuels and Steele for d = 1.
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作者：Harrison, JM
作者单位：Stanford University
摘要：A recent paper by Harrison and Van Mieghem explained in general mathematical terms how one forms an equivalent workload formulation of a Brownian network model. Denoting by Z(t) the state vector of the original Brownian network, one has a lower dimensional state descriptor W(t) = MZ(t) in the equivalent workload formulation, where M can be chosen as any basis matrix for a particular linear space. This paper considers Brownian models for a very general class of open processing net works, and in...
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作者：Graham, C; O'Connell, N
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Hewlett-Packard
摘要：We consider a symmetric network composed of N links, each with capacity C. Calls arrive according to a Poisson process, and each call concerns L distinct links chosen uniformly at random. If each of these links has free capacity, the call is held for an exponential time; otherwise it is lost. The semiexplicit stationary distribution for this process is similar to a Gibbs measure: it involves a normalizing factor, the partition function, which is very difficult to evaluate. We let N go to infin...
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作者：Gärtner, J; König, W
作者单位：Technical University of Berlin
摘要：We consider the parabolic Anderson problem partial derivative (t)u = kappa Deltau + xi (x)u on R+ x R-d with initial condition u(0, x) = 1. Here xi(.) is a random shift-invariant potential having high delta -like peaks on small islands. We express the second-order asymptotics of the pth moment (p is an element of [1, infinity)) of u(t, 0) as t --> infinity in terms of a variational formula involving an asymptotic description of the rescaled shapes of these peaks via their cumulant generating f...
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作者：Coffman, EG; Flatto, L; Jelenkovic, P
作者单位：Alcatel-Lucent; Lucent Technologies; AT&T; Columbia University
摘要：Starting at time 0, unit-length intervals arrive and are placed on the positive real line by a unit-intensity Poisson process in two dimensions; the left endpoints of intervals appear at the rate of 1 per unit time per unit distance. An arrival is accepted if and only if, for some given x, the interval is contained in [0, x] and overlaps no interval already accepted. This stochastic, on-line interval packing problem generalizes the classical parking problem, the latter corresponding only to th...
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作者：Barbour, AD; Ethier, SN; Griffiths, RC
作者单位：University of Zurich; Utah System of Higher Education; University of Utah; Monash University
摘要：Using duality, an expansion is found for the transition function of the reversible K-allele diffusion model in population genetics. In the neutral case, the expansion is explicit but already known. When selection is present, it depends on the distribution at time t of a specified R-type birth-and-death process starting at infinity. The latter process is constructed by means of a coupling argument and characterized as the Ray process corresponding to the Ray-Knight compactification of the K-dim...
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作者：Liu, QS; Rouault, A
作者单位：Universite de Rennes; Universite Paris Saclay
摘要：Let W greater than or equal to 0 be a random variable with EW = 1, and let Z((r)) (r greater than or equal to 2) be the limit of a Mandelbrot's martingale, defined as sums of product of independent random weights having the same distribution as W, indexed by nodes of a homogeneous r-ary tree. We study asymptotic properties of Z((r)) as r --> infinity: we obtain a law of large numbers, a central limit theorem, a result for convergence of moment generating functions and a theorem of large deviat...
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作者：Adler, RJ
作者单位：Technion Israel Institute of Technology
摘要：This is a rambling review of what, with a few notable and significant exceptions, has been a rather dormant area for over a decade. It concentrates on the septuagenarian problem of finding good approximations for the excursion probability P{sup(t is an element ofT) X-t greater than or equal to lambda}, where lambda is large, X is a Gaussian, or Gaussian-like, process over a region T subset of R-N and, generally, N > 1. A quarter of a century ago, there was a flurry of papers out of various sch...
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作者：Perrut, A
作者单位：Universite de Rouen Normandie
摘要：We consider a reaction-diffusion process with two components, on the grid Z. This process had been introduced by Durrett and Levin to describe a two-species interaction. We prove the process admits hydrodynamic limits, first with a technique based on correlation functions, then with the method of relative entropy plus coupling.
