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作者：Albin, JMP
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：We derive upper and lower asymptotic bounds for the distribution of the supremum for a self-similar stochastic process. As an intermediate step, most proofs relate suprema to sojourns before proceeding to an appropriate discrete approximation. Our results rely on one or more of three assumptions, which in turn essentially require weak convergence, existence of a first moment and tightness, respectively. When all three assumptions hold, the upper and lower bounds coincide (Corollary 1). For P-s...
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作者：Norris, JR
作者单位：University of Cambridge
摘要：We consider the class of stationary, zero-mean Gaussian processes, indexed by the circle, satisfying a two-point Markov property and taking values in a vector bundle over the circle with given holonomy. We establish, subject to certain additional symmetry properties, a classification of all such processes. We then propose a construction of a Brownian motion of loops, in which these processes provide the infinitesimal increments.We consider the class of stationary, zero-mean Gaussian processes,...
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作者：Berkes, I; Philipp, W
作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We extend Levy's classical criterion for a sequence of independent identically distributed random variables to belong to the domain of partial attraction of a nondegenerate Gaussian law to stationary phi-mixing sequences. We also extend some results of Kesten and of Kuelbs and Zinn on the LIL behavior of independent identically distributed random variables to stationary phi-mixing sequences. No assumptions on the rate of decay for the mixing coefficient are made.
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作者：Cepa, E
作者单位：Universite de Orleans
摘要：An existence and uniqueness result is proven for a generalization (by introduction of a multivalued maximal monotone operator) of the deterministic Skorohod problem (with normal reflection) associated with a closed convex D in R-d. The maximal monotone operator formulation allows for drifts that blow up as one gets near the boundary. This multivalued approach clarifies the connection between nonlinear semigroup theory and the Skorohod problem. As a consequence, we discuss then the stochastic c...
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作者：Ethier, SN; Kurtz, TG
作者单位：Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison
摘要：Fleming-Viot processes are probability-measure-valued diffusion processes that can be used as stochastic models in population genetics. Here we use duality methods to prove ergodic theorems for Fleming-Viot processes, including those with recombination. Coupling methods are also used to establish ergodicity of Fleming-Viot processes, first without and then with selection. A special type of selection known as symmetric overdominance is treated by other methods.
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作者：Peligrad, M
作者单位：University System of Ohio; University of Cincinnati
摘要：In this paper, we study the weak convergence to an appropriate Gaussian process of the empirical process of the block-based bootstrap estimator proposed by Kunsch for stationary sequences. The classes of processes investigated are weak dependent and associated sequences. We also prove that, differently from the independent situation, the bootstrapped estimator of the mean of certain dependent sequences satisfies the central limit theorem while the mean of the original sequence does not.
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作者：Bertoin, J
作者单位：Sorbonne Universite
摘要：Let xi, xi(1), be i.i.d. real-valued random variables and S-n = xi(1) + ... + xi(n). In the case when the distribution of xi is close to a stable (alpha) law for some alpha is an element of (0, 1) boolean OR (1, 2), we investigate the asymptotic behavior in distribution of the maximum of normalized sums, max(k = 1, ..., n) k(-1/alpha) S-k. This completes the Darling-Erdos limit theorem for the case alpha = 2.
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作者：Deuschel, JD; Rosen, J
作者单位：Technical University of Berlin; City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：We derive a large deviation principle for the occupation time functional, acting on functions with zero Lebesgue integral, for both super-Brownian motion and critical branching Brownian motion in three dimensions. Our technique, based on a moment formula of Dynkin, allows us to compute the exact rate functions, which differ for the two processes. Obtaining the exact rate function for the super-Brownian motion solves a conjecture of Lee and Remillard. We also show the corresponding CLT and obta...
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作者：Hsing, TL; Leadbetter, MR
作者单位：Texas A&M University System; Texas A&M University College Station; University of North Carolina; University of North Carolina Chapel Hill
摘要：The excursion random measure zeta of a stationary process is defined on sets E subset of (-infinity, infinity) x (0, infinity), as the time which the process (suitably normalized) spends in the set E. Particular cases thus include a multitude of features (including sojourn times) related to high levels. It is therefore not surprising that a single limit theorem for zeta at high levels contains a wide variety of useful extremal and high level exceedance results for the stationary process itself...
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作者：Lalley, SP; Sellke, T
作者单位：Purdue University System; Purdue University
摘要：A conjecture of Liggett concerning the regime of weak survival for the contact process on a homogeneous tree is proved. The conjecture is shown to imply that the Hausdorff dimension of the limit set of such a contact process is no larger than half the Hausdorff dimension of the space of ends of the tree. The conjecture is also shown to imply that at the boundary between weak survival and strong survival, the contact process survives only weakly, a theorem previously proved by Zhang. Finally, a...
