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作者：Kardaras, Constantinos
作者单位：Boston University
摘要：We provide an axiomatic foundation for the representation of numeraire-invariant preferences of economic agents acting in a financial market. In a static environment, the simple axioms turn out to be equivalent to the following choice rule: the agent prefers one outcome over another if and only if the expected (under the agent's subjective probability) relative rate of return of the latter outcome with respect to the former is nonpositive. With the addition of a transitivity requirement, this ...
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作者：Bramson, Maury
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：There has recently been considerable interest in the stability of different fair bandwidth sharing policies for models that arise in the context of Internet congestion control. Here, we consider a connection level model, introduced by Massoulie and Roberts [Telecommunication Systems 15 (2000) 185-201], that represents the randomly varying number of flows present in a network. The weighted alpha-fair and weighted max-min fair bandwidth sharing policies are among important policies that have bee...
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作者：Kim, Jeong Han; Montenegro, Ravi; Peres, Yuval; Tetali, Prasad
作者单位：Yonsei University; National Institute for Mathematical Sciences (NIMS), Republic of Korea; Microsoft; University of Massachusetts System; University of Massachusetts Lowell; University System of Georgia; Georgia Institute of Technology
摘要：We show a Birthday Paradox for self-intersections of Markov chains with uniform stationary distribution. As an application, we analyze Pollard's Rho algorithm for finding the discrete logarithm in a cyclic group G and find that if the partition in the algorithm is given by a random oracle, then with high probability a collision occurs in Theta(root vertical bar G vertical bar) steps. Moreover, for the parallelized distinguished points algorithm on J processors we find that Theta(root vertical ...
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作者：Santos, Manuel S.
作者单位：University of Miami; Universidad Carlos III de Madrid
摘要：This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions indexed by a vector of parameters. A key step in the method of proof is to show the uniform convergence (a.s.) of a family of sample distributions over the domain of parameters. This uniform convergence holds under mild continuity and monotonicity conditions on...
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作者：Deaconu, Madalina; Lejay, Antoine
作者单位：Inria; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine
摘要：The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with importance sampling techniques. The first interest of this approach is that the weights can be easily computed from the density of the one-dimensional Brownian motion. Compared to the Euler scheme this method allows one to obtain a more accurate approximation ...
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作者：Cohen, Samuel N.; Elliott, Robert J.
作者单位：University of Adelaide; University of Calgary
摘要：Most previous contributions to BSDEs, and the related theories of nonlinear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Using solutions of BSDEs on spaces related to finite state, continuous time Markov chains, we develop a theory of nonlinear expectations in the spirit of [Dynamically consistent nonlinear evaluations and expectations (2005) Shandong Univ.]. We prove basic properties of these expectations and show their ap...
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作者：Ellis, Richard S.; Machta, Jonathan; Otto, Peter Tak-Hun
作者单位：University of Massachusetts System; University of Massachusetts Amherst; University of Massachusetts System; University of Massachusetts Amherst; Willamette University
摘要：The main focus of this paper is to determine whether the thermodynamic magnetization is a physically relevant estimator of the finite-size magnetization. This is done by comparing the asymptotic behaviors of these two quantities along parameter sequences converging to either a second-order point or the tricritical point in the mean-field Blume-Capel model. We show that the thermodynamic magnetization and the finite-size magnetization are asymptotic when the parameter alpha governing the speed ...
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作者：Limic, Vlada; Volkov, Stanislav
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; University of Bristol
摘要：By a theorem of Volkov [12] we know that on most graphs with positive probability the linearly vertex-reinforced random walk (VRRW) stays within a finite trapping subgraph at all large times. The question of whether this tail behavior occurs with probability one is open in general. In his thesis, Pemantle [5] proved, via a dynamical system approach, that for a VRRW on any complete graph the asymptotic frequency of visits is uniform over vertices. These techniques do not easily extend even to t...
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作者：Barral, Julien; Jin, Xiong; Mandelbrot, Benoit
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris 13; Inria; Yale University
摘要：Positive T-martingales were developed as a general framework that extends the positive measure-valued martingales and are meant to model intermittent turbulence. We extend their scope by allowing the martingale to take complex values. We focus on martingales constructed on the interval T = [0, 1] and replace random measures by random functions. We specify a large class of such martingales for which we provide a general sufficient condition for almost sure uniform convergence to a nontrivial li...
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作者：Coupier, David
作者单位：Universite de Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：A d-dimensional binary Markov random field on a lattice torus is considered. As the size n of the lattice tends to infinity, potentials a = a (n) and b = b(n) depend on n. Precise bounds for the probability for local configurations to occur in a large ball are given. Under some conditions bearing on a (n) and b(n), the distance between copies of different local configurations is estimated according to their weights. Finally, a sufficient condition ensuring that a given local configuration occu...
