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作者：Chan, Hock Peng; Lai, Tze Leung
作者单位：National University of Singapore; Stanford University
摘要：Large deviation theory has provided important clues for the choice of importance sampling measures for Monte Carlo evaluation of exceedance probabilities. However, Glasserman and Wang [Ann. Appl. Probab. 7 (1997) 731-746] have given examples in which importance sampling measures that are consistent with large deviations can perform much worse than direct Monte Carlo. We address this problem by using certain mixtures of exponentially twisted measures for importance sampling. Their asymptotic op...
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作者：Mairesse, Jean; Matheus, Frederic
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：Consider the braid group B-3 = < a, b vertical bar aba = bab > and the nearest neighbor random walk defined by a probability v with support {a, a(-1), b, b(-1)}. The rate of escape of the walk is explicitly expressed in function of the unique solution of a set of eight polynomial equations of degree three over eight indeterminates. We also explicitly describe the harmonic measure of the induced random walk on B-3 quotiented by its center. The method and results apply, mutatis mutandis, to near...
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作者：Jacka, Saul; Berkaoui, Abdelkarem
作者单位：University of Warwick
摘要：We consider trading in a financial market with proportional transaction costs. In the frictionless case, claims are maximal if and only if they are priced by a consistent price process-the equivalent of an equivalent martingale measure. This result fails in the presence of transaction costs. A properly maximal claim is one which does have this property. We show that the properly maximal claims are dense in the set of maximal claims (with the topology of convergence in probability).
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作者：Jaskiewicz, Anna
作者单位：Wroclaw University of Science & Technology
摘要：This paper deals with discrete-time Markov control processes on a general state space. A long-run risk-sensitive average cost criterion is used as a performance measure. The one-step cost function is nonnegative and possibly unbounded. Using the vanishing discount factor approach, the optimality inequality and an optimal stationary strategy for the decision maker are established.
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作者：Chigansky, Pavel; van Handel, Ramon
作者单位：Weizmann Institute of Science; California Institute of Technology
摘要：We investigate the robustness of nonlinear filtering for continuous time finite state Markov chains, observed in white noise, with respect to misspecification of the model parameters. It is shown that the distance between the optimal filter and that with incorrect model parameters converges to zero uniformly over the infinite time interval as the misspecified model converges to the true model, provided the signal obeys a mixing condition. The filtering error is controlled through the exponenti...
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作者：Roitershtein, Alexander
作者单位：University of British Columbia
摘要：For a class of stationary Markov-dependent sequences (A(n), B-n) is an element of R-2, we consider the random linear recursion S-n = A(n) + BnSn-1, n is an element of Z, and show that the distribution tail of its stationary solution has a power law decay.
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作者：Dennert, Florian; Gruebel, Rudolf
作者单位：Leibniz University Hannover
摘要：We show that the number of renewals up to time t exhibits distributional fluctuations as t -> infinity if the underlying lifetimes increase at an exponential rate in a distributional sense. This provides a probabilistic explanation for the asymptotics of insertion depth in random trees generated by a bit-comparison strategy from uniform input; we also obtain a representation for the resulting family of limit laws along subsequences. Our approach can also be used to obtain rates of convergence.
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作者：Janssen, A. J. E. M.; van Leeuwaarden, J. S. H.
作者单位：Philips; Philips Research
摘要：Let X-1, X-2.... be independent variables, each having a normal distribution with negative mean -beta < 0 and variance 1. We consider the partial sums Sn = X-1 + - - - + X-n, with S-0 = 0, and refer to the process {S-n : n >= 0} as the Gaussian random walk. We present explicit expressions for the mean and variance of the maximum M = max{S-n : n > 0}. These expressions are in terms of Taylor series about beta = 0 with coefficients that involve the Riemann zeta function. Our results extend Kingm...
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作者：Heffernan, Janet E.; Resnick, Sidney I.
作者单位：Lancaster University; Cornell University
摘要：Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation provides a rich description of extremal dependence in the case of asymptotic dependence, but fails to distinguish between exact independence and asymptotic independence. Hidden regular variation addresses this problem by requiring components of the random v...
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作者：Hutzenthaler, M.; Wakolbinger, A.
作者单位：Goethe University Frankfurt
摘要：For a class of processes modeling the evolution of a spatially structured population with migration and a logistic local regulation of the reproduction dynamics, we show convergence to an upper invariant measure from a suitable class of initial distributions. It follows from recent work of Alison Etheridge that this upper invariant measure is nontrivial for sufficiently large super-criticality in the reproduction. For sufficiently small super-criticality, we prove local extinction by compariso...
