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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...
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作者：Kyprianou, A. E.; Pardo, J. C.; Rivero, V.
作者单位：University of Bath
摘要：Understanding the space time features of how a Levy process crosses a constant barrier for the first time, and indeed the last time, is a problem which is central to many models in applied probability such as queueing theory, financial and actuarial mathematics, optimal stopping problems, the theory of branching processes, to name but a few. In Doney and Kyprianou [Ann. Appl. Probab. 16 (2006) 91-106] a new quintuple law was established for a general Levy process at first passage below a fixed...
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作者：Kuznetsov, Alexey
作者单位：York University - Canada
摘要：In this paper we introduce a ten-parameter family of Levy processes for which we obtain Wiener-Hopf factors and distribution of the supremum process in semi-explicit form. This family allows an arbitrary behavior of small jumps and includes processes similar to the generalized tempered stable, KoBoL and CGMY processes. Analytically it is characterized by the property that the characteristic exponent is a meromorphic function, expressed in terms of beta and digamma functions. We prove that the ...
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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：The familiar cascade measures are sequences of random positive measures obtained on [0, 1] via b-adic independent cascades. To generalize them, this paper allows the random weights invoked in the cascades to take real or complex values. This yields sequences of random functions whose possible strong or weak limits are natural candidates for modeling multifractal phenomena. Their asymptotic behavior is investigated, yielding a sufficient condition for almost sure uniform convergence to nontrivi...
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作者：Hitczenko, Pawel; Wesolowski, Jacek
作者单位：Drexel University; Warsaw University of Technology
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作者：Ethier, S. N.; Lee, Jiyeon
作者单位：Utah System of Higher Education; University of Utah; Yeungnam University
摘要：The antique Mills Futurity slot machine has two unusual features. First, if a player loses 10 times in a row, the 10 lost coins are returned. Second, the payout distribution varies from coup to coup in a manner that is nonrandom and periodic with period 10. It follows that the machine is driven by a 100-state irreducible period-10 Markov chain. Here, we evaluate the stationary distribution of the Markov chain, and this leads to a strong law of large numbers and a central limit theorem for the ...
