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作者：Dalang, RC; Nualart, E
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We give general sufficient conditions which imply upper and lower bounds for the probability that a multiparameter process hits a given set E in terms of a capacity of E related to the process. This extends a result of Khoshnevisan and Shi [Ann. Probab. 27 (1999) 1135-1159], where estimates for the hitting probabilities of the (N, d) Brownian sheet in terms of the (d - 2N) Newtonian capacity are obtained, and readily applies to a wide class of Gaussian processes. Using Malliavin calculus and, ...
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作者：De La Peña, VH; Klass, MJ; Lai, TL
作者单位：Columbia University; University of California System; University of California Berkeley; Stanford University
摘要：Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment assumptions. In this paper we present several exponential and moment inequalities, particularly those related to laws of the iterated logarithm, for self-normalized random variables including martingales. Tail probability bounds are also derived. For random variables B-t > 0 and A(t), let Y-t(lambda) = ex...
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作者：Manstavicius, M
作者单位：University of Connecticut
摘要：Let xit, t is an element of [0, T], be a strong Markov process with values in a complete separable metric space (X, rho) and with transition probability function P-s,P-t (x, dy), 0 less than or equal to s less than or equal to t less than or equal to T, x is an element of X. For any h is an element of [0, T] and a > 0, consider the function alpha(h,a) = sup{P-s,P-t(x, {y:rho(x,y) greater than or equal to a}):x is an element of X, 0 less than or equal to s less than or equal to t less than or e...
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作者：Fleischmann, K; Swart, JM
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Erlangen Nuremberg
摘要：In a supercritical branching particle system, the trimmed tree consists of those particles which have descendants at all times. We develop this concept in the superprocess setting. For a class of continuous superprocesses with Feller underlying motion on compact spaces, we identify the trimmed tree, which turns out to be a binary splitting particle system with a new underlying motion that is a compensated h-transform of the old one. We show how trimmed trees may be estimated from above by embe...
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作者：Baudoin, F
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We extend to Riemannian manifolds the theory of conditioned stochastic differential equations. We also provide some enlargement formulas for the Brownian filtration in this nonflat setting.
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作者：Alon, N; Benjamini, I; Stacey, A
作者单位：Microsoft; Tel Aviv University; Tel Aviv University; University of Cambridge
摘要：Consider a uniform expanders family G(n) with a uniform bound on the degrees. It is shown that for any p and c > 0, a random subgraph of G(n) obtained by retaining each edge, randomly and independently, with probability p, will have at most one cluster of size at least c\G(n)\, with probability going to one, uniformly in p. The method from Ajtai, Komlos and Szemeredi [Combinatorica 2 (1982) 1-7] is applied to obtain some new results about the critical probability for the emergence of a giant c...
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作者：Mendelson, S; Schechtman, G
作者单位：Australian National University; Weizmann Institute of Science
摘要：We evaluate the shattering dimension of various classes of linear functionals on various symmetric convex sets. The proofs here relay mostly on methods from the local theory of normed spaces and include volume estimates, factorization techniques and tail estimates of norms, viewed as random variables on Euclidean spheres. The estimates of shattering dimensions can be applied to obtain error bounds for certain classes of functions, a fact which was the original motivation of this study. Althoug...
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作者：Slomczynski, W; Zastawniak, T
作者单位：Jagiellonian University; University of Hull
摘要：Expected utility maximization problems in mathematical finance lead to a generalization of the classical definition of entropy. It is demonstrated that a necessary and sufficient condition for the second law of thermodynamics to operate is that any one of the generalized entropies should tend to its minimum value of zero.
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作者：Peccati, G
作者单位：Universite Paris Saclay; Bocconi University
摘要：Consider a (possibly infinite) exchangeable sequence X = {X-n : 1 less than or equal to n < N}, where N is an element of N boolean OR {infinity}, with values in a Borel space (A, A), and note X-n = (X-1,..., X-n). We say that X is Hoeffding decomposable if, for each n, every square integrable, centered and symmetric statistic based on Xn can be written as an orthogonal sum of n U-statistics with degenerated and symmetric kernels of increasing order. The only two examples of Hoeffding decomposa...
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作者：Chen, LHY; Shao, QM
作者单位：National University of Singapore; National University of Singapore; University of Oregon
摘要：We establish both uniform and nonuniform error bounds of the Berry-Esseen type in normal approximation under local dependence. These results are of an order close to the best possible if not best possible. They are more general or sharper than many existing ones in the literature. The proofs couple Stein's method with the concentration inequality approach.
