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作者：Hachem, Walid; Loubaton, Philippe; Najim, Jamal
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Centre National de la Recherche Scientifique (CNRS)
摘要：Consider an N x n random matrix Y-n = (Y-ij(n)) with entries given by Y-ij(n) = sigma(ij)(n)/root n X-ij(n), the X-ij(n) being centered, independent and identically distributed random variables with unit variance and (sigma(ij) (n); 1 <= i <= N, 1 <= j <= n) being an array of numbers we shall refer to as a variance profile. In this article, we study the fluctuations of the random variable log det (Y-n Y-n*+ rho I-N), where Y* is the Hermitian adjoint of Y and rho > 0 is an additional parameter...
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作者：Gabetta, Ester; Regazzini, Eugenio
作者单位：University of Pavia; Consiglio Nazionale delle Ricerche (CNR); Istituto di Matematica Applicata e Tecnologie Informatiche Enrico Magenes (IMATI-CNR)
摘要：We prove that the solution of the Kac analogue of Boltzmann's equation can be viewed as a probability distribution of a sum of a random number of random variables. This fact allows us to study convergence to equilibrium by means of it few classical statements pertaining to the central limit theorem. In particular, a new proof of the convergence to the Maxwellian distribution is provided. with a rate information both under the sole hypothesis that the initial energy is finite and under the addi...
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作者：Barbour, A. D.; Luczak, M. J.
作者单位：University of Zurich; University of London; London School Economics & Political Science
摘要：In modeling parasitic diseases, it is natural to distinguish hosts according to the number of parasites that they carry, leading to a countably infinite type space. Proving the analogue of the deterministic equations, used in models with finitely many types as a law of large numbers approximation to the underlying stochastic model, has previously either been done case by case, using some special structure, or else not attempted. In this paper we prove a general theorem of this sort, and comple...
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作者：Budhiraja, Amarjit; Ross, Kevin
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Stanford University
摘要：A singular stochastic control problem with state constraints in two-dimensions is studied. We show that the value function is C(1) and its directional derivatives are the value functions of certain optimal stopping problems. Guided by the optimal stopping problem, we then introduce the associated no-action region and the free boundary and show that, under appropriate conditions, an optimally controlled process is a Brownian motion in the no-action region with reflection at the free boundary. T...
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作者：Gouere, Jean-Baptiste; Marchand, Regine
作者单位：Universite de Orleans; Universite de Lorraine
摘要：We study a random growth model on R(d) introduced by Deijfen. This is a continuous first-passage percolation model. The growth occurs by means of spherical outbursts with random radii in the infected region. We aim to find conditions on the distribution of the random radii to determine whether the growth of the process is linear or not. To do so, we compare this model with a continuous analogue of the greedy lattice paths model and transpose results for greedy paths from the lattice setting to...
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作者：Liu, Wei-Dong; Lin, Zhengyan; Shao, Qi-Man
作者单位：Zhejiang University; Hong Kong University of Science & Technology
摘要：Let X-1 , . . . , X-n be a random sample from a p-dimensional population distribution. Assume that c(1)n(alpha) <= p <= c(2)n(alpha) for some positive constants c(1), c(2) and alpha. In this paper we introduce a new statistic for testing independence of the p-variates of the population and prove that the limiting distribution is the extreme distribution of type I with a rate of convergence O ((log n)(5/2)/root n). This is much faster than O (1/log n), a typical convergence rate for this type o...
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作者：Dai, J. G.; Lin, Wuqin
作者单位：University System of Georgia; Georgia Institute of Technology; Northwestern University
摘要：We consider a class of stochastic processing networks. Assume that the networks satisfy a complete resource pooling condition. We prove that each maximum pressure policy asymptotically minimizes the workload process in a stochastic processing network in heavy traffic. We also show that, under each quadratic holding cost structure, there is a maximum pressure policy that asymptotically minimizes the holding cost. A key to the optimality proofs is to prove a state space collapse result and a hea...
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作者：Avram, Florin; Palmowski, Zbigniew; Pistorius, Martijn R.
作者单位：Universite de Pau et des Pays de l'Adour; University of Wroclaw; University of London; King's College London
摘要：Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of claims according to a renewal process. One ruin problem considered is that of the corresponding two-dimensional fisk process first leaving the positive quadrant; another is that of entering the negative quadrant. When the claims arrive according to a Poisson process, we obtain a closed form expression for the ultimate r...
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作者：Bielecki, Tomasz R.; Jeanblanc, Monique; Rutkowski, Marek
作者单位：Illinois Institute of Technology; Universite Paris Saclay; University of New South Wales Sydney; Warsaw University of Technology
摘要：In the paper we study dynamics of the arbitrage prices of credit default swaps within a hazard process model of credit risk. We derive these dynamics without postulating that the immersion property is satisfied between some relevant filtrations. These results are then applied so to study the problem of replication of general defaultable claims, including some basket claims, by means of dynamic trading of credit default swaps.
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作者：MacPhee, Iain; Menshikov, Mikhail; Petritis, Dimitri; Popov, Serguei
作者单位：Durham University; Universite de Rennes; Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidade de Sao Paulo
摘要：We consider a polling model with multiple stations, each with Poisson arrivals and a queue of infinite capacity. The service regime is exhaustive and there is Jacksonian feedback of served customers. What is new here is that when the server comes to a station it chooses the service rate and the feedback parameters at random; these remain valid during the whole stay of the server at that station. We give criteria for recurrence, transience and existence of the sth moment of the return time to t...
