-
作者：Johnstone, Iain M.; Ma, Zongming
作者单位：Stanford University; University of Pennsylvania
摘要：We study the rate of convergence for the largest eigenvalue distributions in the Gaussian unitary and orthogonal ensembles to their Tracy-Widom limits. We show that one can achieve an O(N-2/3.) rate with particular choices of the centering and scaling constants. The arguments here also shed light on more complicated cases of Laguerre and Jacobi ensembles, in both unitary and orthogonal versions. Numerical work shows that the suggested constants yield reasonable approximations, even for surpris...
-
作者：Guasoni, Paolo; Robertson, Scott
作者单位：Boston University; Dublin City University; Carnegie Mellon University
摘要：This paper develops a method to derive optimal portfolios and risk premia explicitly in a general diffusion model for an investor with power utility and a long horizon. The market has several risky assets and is potentially incomplete. Investment opportunities are driven by, and partially correlated with, state variables which follow an autonomous diffusion. The framework nests models of stochastic interest rates, return predictability, stochastic volatility and correlation risk. In models wit...
-
作者：Biggins, J. D.
作者单位：University of Sheffield
摘要：This paper gives conditions for the rightmost particle in the nth generation of a multitype branching random walk to have a speed, in the sense that its location divided by n converges to a constant as n goes to infinity. Furthermore, a formula for the speed is obtained in terms of the reproduction laws. The case where the collection of types is irreducible was treated long ago. In addition, the asymptotic behavior of the number in the nth generation to the right of na is obtained. The initial...
-
作者：Berestycki, Nathanael; Pymar, Richard
作者单位：University of Cambridge
摘要：We consider bond percolation on n vertices on a circle where edges are permitted between vertices whose spacing is at most some number L = L(n). We show that the resulting random graph gets a giant component when L >> (log n)(2) (when the mean degree exceeds 1) but not when L << log n. The proof uses comparisons to branching random walks. We also consider a related process of random transpositions of n particles on a circle, where transpositions only occur again if the spacing is at most L. Th...
-
作者：Budhiraja, Amarjit; Ghosh, Arka P.
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Iowa State University
摘要：Scheduling control problems for a family of unitary networks under heavy traffic with general interarrival and service times, probabilistic routing and an infinite horizon discounted linear holding cost are studied. Diffusion control problems, that have been proposed as approximate models for the study of these critically loaded controlled stochastic networks, can be regarded as formal scaling limits of such stochastic systems. However, to date, a rigorous limit theory that justifies the use o...
-
作者：Shah, Devavrat; Shin, Jinwoo
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：There has recently been considerable interest in design of low-complexity, myopic, distributed and stable scheduling algorithms for constrained queueing network models that arise in the context of emerging communication networks. Here we consider two representative models. One, a queueing network model that captures randomly varying number of packets in the queues present at a collection of wireless nodes communicating through a shared medium. Two, a buffered circuit switched network model for...
-
作者：Kuznetsov, A.; Kyprianou, A. E.; Pardo, J. C.
作者单位：York University - Canada; University of Bath
摘要：The last couple of years has seen a remarkable number of new, explicit examples of the Wiener-Hopf factorization for Levy processes where previously there had been very few. We mention, in particular, the many cases of spectrally negative Levy processes in [Sixth Seminar on Stochastic Analysis, Random Fields and Applications (2011) 119-146, Electron. J. Probab. 13 (2008) 1672-1701], hyper-exponential and generalized hyper-exponential Levy processes [Quant. Finance 10 (2010) 629-644], Lamperti-...
-
作者：Mossel, Elchanan; Roch, Sebastien
作者单位：University of California System; University of California Berkeley; University of California System; University of California Los Angeles; University of California System; University of California Los Angeles
摘要：The reconstruction of phylogenies from DNA or protein sequences is a major task of computational evolutionary biology. Common phenomena, notably variations in mutation rates across genomes and incongruences between gene lineage histories, often make it necessary to model molecular data as originating from a mixture of phylogenies. Such mixed models play an increasingly important role in practice. Using concentration of measure techniques, we show that mixtures of large trees are typically iden...
-
作者：Jiang, Yunjiang
作者单位：Stanford University
摘要：We show that the classical Kac's random walk on (n - 1)-sphere Sn-1 starting from the point mass at e(1) mixes in O(n(5)(log n)(3)) steps in total variation distance. The main argument uses a truncation of the running density after a burn-in period, followed by L-2 convergence using the spectral gap information derived by other authors. This improves upon a previous bound by Diaconis and Saloff-Coste of order O(n(2n)).
-
作者：Pages, Gilles; Panloup, Fabien
作者单位：Sorbonne Universite; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse
摘要：We extend to Lipschitz continuous functionals either of the true paths or of the Euler scheme with decreasing step of a wide class of Brownian ergodic diffusions, the central limit theorems formally established for their marginal empirical measure of these processes (which is classical for the diffusions and more recent as concerns their discretization schemes). We illustrate our results by simulations in connection with barrier option pricing.
