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作者：Shah, D.; Tsitsiklis, J. N.; Zhong, Y.
作者单位：Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley
摘要：We consider a flow-level model of a network operating under an a-fair bandwidth sharing policy (with alpha > 0) proposed by Roberts and Massoulie [Telecomunication Systems 15 (2000) 185-201]. This is a probabilistic model that captures the long-term aspects of bandwidth sharing between users or flows in a communication network. We study the transient properties as well as the steady-state distribution of the model. In particular, for alpha >= 1, we obtain bounds on the maximum number of flows ...
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作者：Diaconis, Persi; Fulman, Jason; Holmes, Susan
作者单位：Stanford University; Stanford University; University of Southern California
摘要：Many casinos routinely use mechanical card shuffling machines. We were asked to evaluate a new product, a shelf shuffler. This leads to new probability, new combinatorics and to some practical advice which was adopted by the manufacturer. The interplay between theory, computing, and real-world application is developed.
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作者：Glover, Kristoffer; Hulley, Hardy; Peskir, Goran
作者单位：University of Technology Sydney; University of Manchester
摘要：Let X = (X-t)(t >= 0) be a transient diffusion process in (0, infinity) with the diffusion coefficient sigma > 0 and the scale function L such that X-t -> infinity as t -> infinity, let I-t denote its running minimum for t >= 0, and let theta denote the time of its ultimate minimum I infinity. Setting c(i, x) = 1 - 2L(x)/L(i) we show that the stopping time tau(*) = inf{t >= 0 vertical bar X-t >= f(*)(I-t)} minimizes E(vertical bar theta - tau vertical bar - theta) over all stopping times tau o...
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作者：Harper, Adam J.
作者单位：University of Cambridge
摘要：We prove new lower bounds for the upper tail probabilities of suprema of Gaussian processes. Unlike many existing bounds, our results are not asymptotic, but supply strong information when one is only a little into the upper tail. We present an extended application to a Gaussian version of a random process studied by Halasz. This leads to much improved lower bound results for the sum of a random multiplicative function. We further illustrate our methods by improving lower bounds for some class...
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作者：Lambert, Amaury; Popovic, Lea
作者单位：Sorbonne Universite; Concordia University - Canada
摘要：We define a doubly infinite, monotone labeling of Bienayme-Galton-Watson (BOW) genealogies. The genealogy of the current generation backwards in time is uniquely determined by the coalescent point process (At; i >= 1), where A(i) is the coalescence time between individuals i and i + 1. There is a Markov process of point measures (8(i); i >= 1) keeping track of more ancestral relationships, such that A(i) is also the first point mass of B-i. This process of point measures is also closely relate...
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作者：Hobson, David; Klimmek, Martin
作者单位：University of Warwick
摘要：The Azema-Yor solution (resp., the Perkins solution) of the Skorokhod embedding problem has the property that it maximizes (resp., minimizes) the law of the maximum of the stopped process. We show that these constructions have a wider property in that they also maximize (and minimize) expected values for a more general class of bivariate functions F(W-tau, S-tau) depending on the joint law of the stopped process and the maximum. Moreover, for monotonic functions g, they also maximize and minim...
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作者：Matoussi, Anis; Possamai, Dylan; Zhou, Chao
作者单位：Centre National de la Recherche Scientifique (CNRS); Le Mans Universite; Institut Polytechnique de Paris; Ecole Polytechnique; Universite PSL; Universite Paris-Dauphine
摘要：In this article, we build upon the work of Soner, Touzi and Zhang [Probab. Theory Related Fields 153 (2012) 149-190] to define a notion of a second order backward stochastic differential equation reflected on a lower cadlag obstacle. We prove existence and uniqueness of the solution under a Lipschitz-type assumption on the generator, and we investigate some links between our reflected 2BSDEs and nonclassical optimal stopping problems. Finally, we show that reflected 2BSDEs provide a super-hedg...
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作者：Soner, H. Mete; Touzi, Nizar; Zhang, Jianfeng
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Swiss Finance Institute (SFI); Institut Polytechnique de Paris; Ecole Polytechnique; University of Southern California
摘要：This paper provides a new formulation of second order stochastic target problems introduced in [SIAM J. Control Optim. 48 (2009) 2344-2365] by modifying the reference probability so as to allow for different scales. This new ingredient enables us to prove a dual formulation of the target problem as the supremum of the solutions of standard backward stochastic differential equations. In particular, in the Markov case, the dual problem is known to be connected to a fully nonlinear, parabolic par...
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作者：Imkeller, Peter; Namachchivaya, N. Sri; Perkowski, Nicolas; Yeong, Hoong C.
作者单位：Humboldt University of Berlin; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We propose a homogenized filter for multiscale signals, which allows us to reduce the dimension of the system. We prove that the nonlinear filter converges to our homogenized filter with rate root epsilon. This is achieved by a suitable asymptotic expansion of the dual of the Zakai equation, and by probabilistically representing the correction terms with the help of BDSDEs.
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作者：Budhiraja, Amarjit; Reinhold, Dominik
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Clark University
摘要：Near critical catalyst-reactant branching processes with controlled immigration are studied. The reactant population evolves according to a branching process whose branching rate is proportional to the total mass of the catalyst. The bulk catalyst evolution is that of a classical continuous time branching process; in addition there is a specific form of immigration. Immigration takes place exactly when the catalyst population falls below a certain threshold, in which case the population is ins...
