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作者：Hennion, H; Hervé, L
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes; Universite de Rennes
摘要：Let M be a noncompact metric space in which every closed ball is compact, and let G be a semigroup of Lipschitz mappings of M. Denote by (Y-n)(ngreater than or equal to1) a sequence of independent G-valued, identically distributed random variables (r.v.'s), and by Z an M-valued r.v. which is independent of the r.v. Y-n, n greater than or equal to 1. We consider the Markov chain (Z(n))(ngreater than or equal to0) with state space M which is defined recursively by Z(0) = Z and Z(n+1) = Y(n+1)Z(n...
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作者：Jeganathan, P
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore
摘要：Consider a sequence X-k = Sigma(j=0) (infinity) c(j)xi(k-j) k greater than or equal to 1, where c(j), j greater than or equal to 0, is a sequence of constants and xi(j), -infinity < j < infinity, is a sequence of independent identically distributed (i.i.d.) random variables (r.v.s) belonging to the domain of attraction of a strictly stable law with index 0 < alpha < 2. Let S-k = Sigma(j=1)(k) X-j. Under suitable conditions on the constants c(j) it is known that for a suitable normalizing const...
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作者：Limic, V; Pemantle, R
作者单位：University of British Columbia; University of Pennsylvania
摘要：The purpose of this note is to provide proofs for some facts about the NK model of evolution proposed by Kauffman and Levin. In the case of normally distributed fitness summands, some of these facts have been previously conjectured and heuristics given. In particular, we provide rigorous asymptotic estimates for the number of local fitness maxima in the case when K is unbounded. We also examine the role of the individual fitness distribution and find the model to be quite robust with respect t...
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作者：Pipiras, V; Taqqu, MS
作者单位：Boston University
摘要：We study stationary stable processes related to periodic and cyclic flows in the sense of Rosinski [Ann. Probab. 23 (1995) 1163-1187]. These processes are not ergodic. We provide their canonical representations, consider examples and show how to identify them among general stationary stable processes. We conclude with the unique decomposition in distribution of stationary stable processes into the sum of four major independent components: 1. A mixed moving average component. 2. A harmonizable ...
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作者：Berti, P; Pratelli, L; Rigo, P
作者单位：Universita di Modena e Reggio Emilia; University of Pavia
摘要：A new type of stochastic dependence for a sequence of random variables is introduced and studied. Precisely, (X-n)ngreater than or equal to1 is said to be conditionally identically distributed (c.i.d.), with respect to a filtration (g(n))(ngreater than or equal to0), if it is adapted to (g(n))(ngreater than or equal to0) and, for each ngreater than or equal to0, (X-k)(k>n) is identically distributed given the past g(n). In case g(0) = {theta, Omega} and g(n) = sigma(X-1,...,X-n), a result of K...
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作者：Jacod, J
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We study the Euler scheme for a stochastic differential equation driven by a Levy process Y. More precisely, we look at the asymptotic behavior of the normalized error process u(n) (X-n - X), where X is the true solution and X-n is its Euler approximation with stepsize 1/n, and u(n) is an appropriate rate going to infinity: if the normalized error processes converge, or are at least tight, we say that the sequence (u(n)) is a rate, which, in addition, is sharp when the limiting process (or pro...
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作者：Chen, ZQ; Fitzsimmons, PJ; Takeda, M; Ying, J; Zhang, TS
作者单位：University of Washington; University of Washington Seattle; Tohoku University; University of California System; University of California San Diego; Fudan University; University of Manchester
摘要：We study Girsanov's theorem in the context of symmetric Markov processes, extending earlier work of Fukushima-Takeda and Fitzsimmons on Girsanov transformations of gradient type. We investigate the most general Girsanov transformation leading to another symmetric Markov process. This investigation requires an extension of the forward-backward martingale method of Lyons-Zheng, to cover the case of processes with jumps.
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作者：De Acosta, A
作者单位：University System of Ohio; Case Western Reserve University
摘要：We refine the conditions for the lower bound in an abstract large deviation result with nonconvex rate function we had previously introduced. We apply the results to certain stochastic recursive schemes.
