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作者：Inoue, A
作者单位：Hokkaido University
摘要：We prove a simple asymptotic formula for partial autocorrelation functions of fractional ARIMA processes.
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作者：Comets, F; Fernández, R; Ferrari, PA
作者单位：Universite Paris Cite; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); Universidade de Sao Paulo
摘要：We present a perfect simulation algorithm for stationary processes indexed by Z, with summable memory decay. Depending on the decay, we construct the process on finite or semi-infinite intervals, explicitly from an i.i.d. uniform sequence. Even though the process has infinite memory, its value at time 0 depends only on a finite, but random, number of these uniform variables. The algorithm is based on a recent regenerative construction of these measures by Ferrari, Maass, Martinez and Ney. As a...
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作者：Jordan, J
作者单位：University of Oxford
摘要：We consider a class of probabilistic models obtained by iterating random functions of k random variables. We prove an analogue of the weak law of large numbers and under a symmetry condition we prove a strong law. The symmetry condition is satisfied if the initial random variables are exchangeable. Our results can be used to give stronger results than those previously obtained in the special case where the function is deterministic. Both types of models have applications in physics and in comp...
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作者：Boyarchenko, S; Levendorskii, S
作者单位：University of Texas System; University of Texas Austin; Southern Federal University; Rostov State University of Economics
摘要：We derive explicit formulas for barrier options of European type and touch-and-out options assuming that under a chosen equivalent martingale measure the stock returns follow a Levy process from a wide class, which contains Brownian motions (BM), normal inverse Gaussian processes (NIG), hyperbolic processes (HP), normal tilted stable Levy processes (NTS Levy), processes of the KoBoL family and any finite mixture of independent BM, NIG, HP, NTS Levy and KoBoL processes. In contrast to the Gauss...
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作者：Toomey, F
作者单位：Dublin Institute for Advanced Studies
摘要：A topical operator on R-d is one which is isotone and homogeneous. Let {A(n) : n greater than or equal to 1} be a sequence of i.i.d. random topical operators such that the projective radius of A(n)...A(1) is almost surely bounded for large n. If {x (n) : n greater than or equal to 1} is a sequence of vectors given by x (n) = A (n)...A(1)x(0), for some fixed initial condition x(0), then the sequence {x(n)/n:n greater than or equal to 1} satisfies a weak large deviation principle. As corollaries...
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作者：Madras, N; Randall, D
作者单位：York University - Canada; University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology
摘要：In this paper we develop tools for analyzing the rate at which a reversible Markov chain converges to stationarity. Our techniques are useful when the Markov chain can be decomposed into pieces which are themselves easier to analyze. The main theorems relate the spectral gap of the original Markov chains to the spectral gaps of the pieces. In the first case the pieces are restrictions of the Markov chain to subsets of the state space; the second case treats a Metropolis-Hastings chain whose eq...
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作者：Takemura, A; Kuriki, S
作者单位：University of Tokyo; Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
摘要：Consider a Gaussian random field with a finite Karhunen-Loeve expansion of the form Z(u) = Sigma(i=1)(n) u(i)z(i), where z(i), i = 1,..., n, are independent standard normal variables and u = (u(1),..., u(n))' ranges over an index set M, which is a subset of the unit sphere Sn-1 in R-n. Under a very general assumption that M is a manifold with a piecewise smooth boundary, we prove the validity and the equivalence of two currently available methods for obtaining the asymptotic expansion of the t...
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作者：Jourdain, B; Martini, C
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Inria
摘要：In mathematical finance, the price of the so-called American Put option is given by the value function of the optimal-stopping problem with the option payoff psi: x --> (K - x)(+) as a reward function. Even in the Black-Scholes model, no closed-formula is known and numerous numerical approximation methods have been specifically designed for this problem. In this paper, as an application of the theoretical result of B. Jourdain and C. Martini [Ann. Inst. Henri Paincare Anal. Nonlinear 18 (2001)...
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作者：Lowe, M; Matzinger, H
摘要：Kesten has observed that the known reconstruction methods of random sceneries seem to strongly depend on the one-dimensional setting of the problem and asked whether a construction still is possible in two dimensions. In this paper we answer this question in the affirmative under the condition that the number of colors in the scenery is large enough.
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作者：Collamore, JF
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Let {(X-n, S-n):n = 0, 1,...} be a Markov additive process, where {x(n)} is a Markov chain on a general state space and S-n is an additive component on R-d. We consider P{S-n is an element of A/epsilon, some n} as epsilon --> 0, where A subset of R-d is open and the mean drift of {S-n} is away from A. Our main objective is to study the simulation of P{S-n is an element of A/epsilon, some n} using the Monte Carlo technique of importance sampling, If the set A is convex, then we establish (i) th...
