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作者：Bentkus, V
作者单位：Vilnius University; Vytautas Magnus University
摘要：In a celebrated work by Hoeffding [J. Amer Statist. Assoc. 58 (1963) 13-30], several inequalities for tail probabilities of sums Mn = X-1 +... + X-n of bounded independent random variables X-j were proved. These inequalities had a considerable impact on the development of probability and statistics, and remained unimproved until 1995 when Talagrand [Inst. Hautes Etudes Sci. Publ. Math. 81 (1995a) 73-205] inserted certain missing factors in the bounds of two theorems. By similar factors, a thir...
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作者：Houdré, C; Marchal, P
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); University System of Georgia; Georgia Institute of Technology; Universite PSL; Ecole Normale Superieure (ENS)
摘要：Concentration of measure is studied, and obtained, for stable and related random vectors.
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作者：Comets, F; Zeitouni, O
作者单位：Universite Paris Cite; University of Minnesota System; University of Minnesota Twin Cities
摘要：We prove a law of large numbers for a class of ballistic, multidimensional random walks in random environments where the environment satisfies appropriate mixing conditions, which hold when the environment is a weak mixing field in the sense of Dobrushin and Shlosman. Our result holds if the mixing rate balances moments of some random times depending on the path. It applies in the nonnestling case, but we also provide examples of nestling walks that satisfy our assumptions. The derivation is b...
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作者：Hu, YZ; Mohammed, SEA; Yan, F
作者单位：University of Kansas; Southern Illinois University System; Southern Illinois University
摘要：In this paper, we develop a strong Milstein approximation scheme for solving stochastic delay differential equations (SDDEs). The scheme has convergence order 1. In order to establish the scheme, we prove an infinite-dimensional Ito formula for tame functions acting on the segment process of the solution of an SDDE. It is interesting to note that the presence of the memory in the SDDE requires the use of the Malliavin calculus and the anticipating stochastic analysis of Nualart and Pardoux. Gi...
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作者：Giné, E; Koltchinskii, V; Zinn, J
作者单位：University of Connecticut; University of Connecticut; University of New Mexico; Texas A&M University System; Texas A&M University College Station; University of Washington; University of Washington Seattle; Sorbonne Universite
摘要：Let fin denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let Psi(t) be a positive continuous function such that parallel toPsif(beta)parallel toinfinity < infinity for some 0 < beta < 1/2. Under natural smoothness conditions, necessary and sufficient conditions for the sequence rootnh(n)(d)/2\logh(n)(d)\ parallel toPsi(t)(f(n)(t) - Efn(t))parallel toinfinity to be stochastically bounded and to converge a.s. to a constant are obtained. Also, the...
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作者：Xiong, J
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：We study a nonlinear stochastic partial differential equation whose solution is the conditional log-Laplace functional of a superprocess in a random environment. We establish its existence and uniqueness by smoothing out the nonlinear term and making use of the particle system representation developed by Kurtz and Xiong [Stochastic Process. Appl. 83 (1999) 103-126]. We also derive the Wong-Zakai type approximation for this equation. As an application, we give a direct proof of the moment formu...
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作者：Doney, RA
作者单位：University of Manchester
摘要：Using the Wiener-Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Levy process above and below by the paths of two random walks. These walks have the same step distribution, but different random starting points. In principle, this allows one to deduce Levy process versions of many known results about the large-time behavior of random walks. This is illustrated by establishing a comprehensive theorem about Levy processes which converge to infinity in probabi...
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作者：Samorodnitsky, G
作者单位：Cornell University
摘要：We study the partial maxima of stationary alpha-stable processes. We relate their asymptotic behavior to the ergodic theoretical properties of the flow. We observe a sharp change in the asymptotic behavior of the sequence of partial maxima as flow changes from being dissipative to being conservative, and argue that this may indicate a change from a short memory process to a long memory process.
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作者：Becker-Kern, P; Meerschaert, MM; Scheffler, HP
作者单位：Dortmund University of Technology; Nevada System of Higher Education (NSHE); University of Nevada Reno
摘要：Scaling limits of continuous time random walks are used in physics to model anomalous diffusion, in which a cloud of particles spreads at a different rate than the classical Brownian motion. Governing equations for these limit processes generalize the classical diffusion equation. In this article, we characterize scaling limits in the case where the particle jump sizes and the waiting time between jumps are dependent. This leads to an efficient method of computing the limit, and a surprising c...
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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...
