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作者：Jacob, Pierre E.; Ryder, Robin J.
作者单位：National University of Singapore; Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris; Universite PSL; Universite Paris-Dauphine
摘要：The Wang-Landau algorithm aims at sampling from a probability distribution, while penalizing some regions of the state space and favoring others. It is widely used, but its convergence properties are still unknown. We show that for some variations of the algorithm, the Wang-Landau algorithm reaches the so-called flat histogram criterion in finite time, and that this criterion can be never reached for other variations. The arguments are shown in a simple context-compact spaces, density function...
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作者：Broniatowski, Michel; Caron, Virgile
作者单位：Sorbonne Universite
摘要：This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a function of its summands as their number tends to infinity. In the large deviation range of the conditioning event it extends the Gibbs conditional principle in the sense that it provides a description of the distribution of the random walk on long subsequences. An approximation of the density of the runs is also obtained when the conditioning event states t...
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作者：Atar, Rami; Biswas, Anup
作者单位：Technion Israel Institute of Technology
摘要：A multi-class single-server system with general service time distributions is studied in a moderate deviation heavy traffic regime. In the scaling limit, an optimal control problem associated with the model is shown to be governed by a differential game that can be explicitly solved. While the characterization of the limit by a differential game is akin to results at the large deviation scale, the analysis of the problem is closely related to the much studied area of control in heavy traffic a...
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作者：Li, Libo; Rutkowski, Marek
作者单位：University of Sydney; Warsaw University of Technology
摘要：We deal with various alternative decompositions of F-martingales with respect to the filtration G, which represents the enlargement of a filtration F by a progressive flow of observations of a random time that either belongs to the class of pseudo-honest times or satisfies the extended density hypothesis. Several related results from the existing literature are revisited and essentially extended. Results on G-semimartingale decompositions of F-local martingales are crucial for applications in ...
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作者：Lijoi, Antonio; Prunster, Igor; Walker, Stephen G.
作者单位：University of Pavia; University of Turin; University of Texas System; University of Texas Austin; Collegio Carlo Alberto
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作者：Akyildirim, Erdinc; Dolinsky, Yan; Soner, H. Mete
作者单位：Borsa Istanbul; Swiss Federal Institutes of Technology Domain; ETH Zurich; Hebrew University of Jerusalem
摘要：A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov process. The first two components are related to the stock and volatility processes and take values in a two-dimensional binomial tree. The other two components of the Markov process are the increments of random walks with simple values in {-1, +1}. The result...
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作者：Pillai, Natesh S.; Yin, Jun
作者单位：Harvard University; University of Wisconsin System; University of Wisconsin Madison
摘要：In this paper we prove the universality of covariance matrices of the form H-NxN=X+ X where X is an M x N rectangular matrix with independent real valued entries x(ij) satisfying Ex(ij)=0 and Ex(ij)(2)=1/M, N, M ->infinity. Furthermore it is assumed that these entries have sub-exponential tails or sufficiently high number of moments. We will study the asymptotics in the regime N/M=d(N) is an element of (0,infinity), lim(N ->infinity) d(N)not equal 0, infinity. Our main result is the edge unive...
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作者：Crisan, Dan; Manolarakis, Konstantinos
作者单位：Imperial College London
摘要：We propose a second order discretization for backward stochastic differential equations (BSDEs) with possibly nonsmooth boundary data. When implemented, the discretization method requires essentially the same computational effort with the Euler scheme for BSDEs of Bouchard and Touzi [Stochastic Process. Appl. 111 (2004) 175-206] and Zhang [Ann. AppL Probab. 14 (2004) 459-488]. However, it enjoys a second order asymptotic rate of convergence, provided that the coefficients of the equation are s...
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作者：Louidor, Oren; Tessler, Ran; Vandenberg-Rodes, Alexander
作者单位：Technion Israel Institute of Technology; Hebrew University of Jerusalem; University of California System; University of California Irvine
摘要：We consider the Williams-Bjerknes model, also known as the biased voter model on the d-regular tree T-d, where d >= 3. Starting from an initial of healthy and infected vertices, infected vertices infect their neighbors at Poisson rate lambda >= 1, while healthy vertices heal their neighbors at Poisson rate 1. All vertices act independently. It is well known that starting from a configuration with a positive but finite number of infected vertices, infected vertices will continue to exist at all...
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作者：Benaim, Michel; Le Borgne, Stephane; Malrieu, Florent; Zitt, Pierre-Andre
作者单位：University of Neuchatel; Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
摘要：Consider the random process (X-t)(t >= 0) solution of (X) over dot(t) = A(It) X-t, where (I-t)(t >= 0) is a Markov process on {0, 1}, and A(0) and A(1) are real Hurwitz matrices on R-2. Assuming that there exists lambda is an element of (0, 1) such that (1 - lambda)A(0) + lambda A(1) has a positive eigenvalue, we establish that parallel to X-t parallel to may converge to 0 or +infinity depending on the jump rate of the process I. An application to product of random matrices is studied. This pa...
