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作者：Mattingly, Jonathan C.; Pillai, Natesh S.; Stuart, Andrew M.
作者单位：Duke University; Duke University; Harvard University; University of Warwick
摘要：Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying computational complexity. In particular, they lead directly to precise estimates of the number of steps required to explore the target measure, in stationarity, as a function of the dimension of the state space. However, to date such results have mainly been proved for target measures with a product structure, severely limiting their applicability. The purpose of this paper is to study diffusion ...
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作者：Lember, Jueri; Matzinger, Heinrich; Torres, Felipe
作者单位：University of Tartu; University System of Georgia; Georgia Institute of Technology; University of Bielefeld
摘要：We consider a general class of superadditive scores measuring the similarity of two independent sequences of n i.i.d. letters from a finite alphabet. Our object of interest is the mean score by letter l(n). By subadditivity l(n) is nondecreasing and converges to a limit l. We give a simple method of bounding the difference l - l(n) and obtaining the rate of convergence. Our result generalizes the previous result of Alexander [Ann. Appl. Probab. 4 (1994) 1074-1082], where only the special case ...
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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-...
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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.
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作者：Martinelli, Fabio; Sinclair, Alistair
作者单位：Roma Tre University; University of California System; University of California Berkeley
摘要：We analyze the mixing time of a natural local Markov chain (the Glauber dynamics) on configurations of the solid-on-solid model of statistical physics. This model has been proposed, among other things, as an idealization of the behavior of contours in the Ising model at low temperatures. Our main result is an upper bound on the mixing time of (O) over tilde (n(3.5)), which is tight within a factor of (O) over tilde(root n). The proof, which in addition gives some insight into the actual evolut...
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作者：Wood, Philip Matchett
作者单位：Stanford University
摘要：The universality phenomenon asserts that the distribution of the eigenvalues of random matrix with i.i.d. zero mean, unit variance entries does not depend on the underlying structure of the random entries. For example, a plot of the eigenvalues of a random sign matrix, where each entry is +1 or -1 with equal probability, looks the same as an analogous plot of the eigenvalues of a random matrix where each entry is complex Gaussian with zero mean and unit variance. In the current paper, we prove...
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作者：Adler, Robert J.; Blanchet, Jose H.; Liu, Jingchen
作者单位：Technion Israel Institute of Technology; Columbia University; Columbia University
摘要：Our focus is on the design and analysis of efficient Monte Carlo methods for computing tail probabilities for the suprema of Gaussian random fields, along with conditional expectations of functionals of the fields given the existence of excursions above high levels, b. Naive Monte Carlo takes an exponential, in b, computational cost to estimate these probabilities and conditional expectations for a prescribed relative accuracy. In contrast, our Monte Carlo procedures achieve, at worst, polynom...
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作者：Addario-Berry, Louigi; Griffiths, Simon; Kang, Ross J.
作者单位：McGill University; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Durham University
摘要：We study invasion percolation on Aldous' Poisson-weighted infinite tree, and derive two distinct Markovian representations of the resulting process. One of these is the sigma -> infinity limit of a representation discovered by Angel et al. [Ann. Appl. Probab. 36 (2008) 420-466]. We also introduce an exploration process of a randomly weighted Poisson incipient infinite cluster. The dynamics of the new process are much more straightforward to describe than those of invasion percolation, but it t...
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作者：Chassagneux, Jean-Francois; Elie, Romuald; Kharroubi, Idris
作者单位：Universite Paris Saclay; Institut Polytechnique de Paris; ENSAE Paris; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In this paper, we study the discrete-time approximation of multidimensional reflected BSDEs of the type of those presented by Hu and Tang [Probab. Theory Related Fields 147 (2010) 89-121] and generalized by Hamadene and Zhang [Stochastic Process. Appl. 120 (2010) 403-426]. In comparison to the penalizing approach followed by Hamadene and Jeanblanc [Math. Oper Res. 32 (2007) 182-192] or Elie and Kharroubi [Statist. Probab. Lett. 80 (2010) 1388-1396], we study a more natural scheme based on obli...
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作者：Oshima, Kojiro; Techmann, Josef; Veluscek, Dejan
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Fujiwara's method can be considered as an extrapolation method of order 6 of the Ninomiya-Victoir weak approximation scheme for the numerical approximation of solution processes of SDEs. We present an extension of Fujiwara's method for arbitrarily high orders, which embeds the original Fujiwara method as the order 6 case. The approach can be considered as a variant of Richardson extrapolation, which allows one to reach high orders with few extrapolation steps. The most important contribution o...
