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作者：DELTIO, PR; BLANCO, MCV
摘要：Let P = (p(ij)), i,j = 1,2,...,n be the matrix of a recurrent Markov chain with stationary vector upsilon > 0 and let R = (r(ij)), i, j = 1,2,...,n be a matrix, where r(ij) = upsilon-(i)p(ij). If R is a symmetric matrix, we improve Alpern's rotational representation of P. By this representation we characterize the reversible Markov chains.
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作者：MEERSCHAERT, MM
摘要：Regular variation is used to study the asymptotic behavior of norming operators for generalized domains of attraction. This leads to a powerful decomposition theorem. Applications include a complete, concise description of moment behavior, centering constants, convergence criteria and tail behavior for generalized domains of attraction.
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作者：HOUDRE, C
摘要：We develop the linear least squares prediction theory for some classes of nonstationary processes having a Fourier spectral representation. We study time domain as well as spectral domain properties for these processes, such as a Wold decomposition and a decomposition for matrix bimeasures. We also obtain an autoregressive representation for the optimum predictor.
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作者：KALLENBERG, O
摘要：Ustunel and Zakai have recently obtained a necessary and sufficient condition for two multiple Wiener integrals with respect to the same Brownian motion to be independent. In the present note, the sufficiency of their condition is shown to be a simple consequence of the classical relationship between multiple Wiener integrals and Hermite polynomials. The original proofs use Malliavin calculus.
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作者：COGBURN, R
摘要：A functional central limit theorem is established for Markov chains in random environments under the assumption of existence of a finite invariant, ergodic measure and a mixing condition. These conditions are always satisfied when the state space is finite.
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作者：GLOVER, J
摘要：The symmetry groups of the potential theory of a Markov process X(t) are used to introduce new algebraic and topological structures on the state space and the process. For example, let G be the collection of bijections phi on E which preserve the collection of excessive functions. Assume there is a transitive subgroup H of the symmetry group G such that the only map phi-epsilon-H fixing a point e epsilon-E is the identity map on E. There is a bijection PSI: E --> H so that the algebraic struct...
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作者：SHORACK, GR
摘要：A huge body of if and only if theorems can be obtained based on certain strong embedding theorems for the partial sum process S(n) and the uniform empirical and quantile processes U(n) and V(n). This embedding was accomplished in 1986 by M. Csorgo, S. Csorgo, L. Horvath and D. Mason. Their embedding is beautifully formulated so that many necessary and sufficient type results can be established using it. It is worthwhile to have an accessible proof. Indeed, these authors have since produced two...
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作者：GOTZE, F
摘要：Berry-Esseen theorems are proved in the multidimensional central limit theorem without using Fourier methods. An effective and simple estimate of the error in the CLT for sums and convex sets using Stein's method and induction is derived. Furthermore, the error in the CLT for multivariate functions of independent random elements is estimated extending results of van Zwet and Friedrich to the multivariate case.
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作者：BALDI, P
摘要：We consider a family of periodic diffusion processes in R(n) with homogenization and a small parameter multiplying the diffusion coefficient. We establish a large deviations principle and as an application we derive an interated logarithm law for periodic diffusions.
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作者：GINE, E; ZINN, J
作者单位：City University of New York (CUNY) System; College of Staten Island (CUNY); Texas A&M University System; Texas A&M University College Station
摘要：It is proved that, for classes of functions F satisfying some measurability, the empirical processes indexed by F and based on P member-of P(S) satisfy the central limit theorem uniformly in P member-of P(S) if and only if the P-Brownian bridges G(P) indexed by F are sample bounded and rho-p uniformly continuous uniformly in P member-of P(S). Uniform exponential bounds for empirical processes indexed by universal bounded Donsker and uniform Donsker classes of functions are also obtained.
