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作者：HOGLUND, T
摘要：We derive an asymptotic approximation of the joint distribution prob(N(u) - n is-an-element-of A, S(N(u)) - u is-element-of B) as n and u --> infinity. Here N(u) = min{n; S(n) > u} denotes the first passage time for a random walk of the form S(n) = SIGMA-k = 1n U(k)(xi-k - 1, xi-k), where xi-0, xi-1,... is a finite Markov chain and where {U(k)(i, j)} infinity(k = 1) is a sequence of independent random variables. The approximation holds for all sets B and a fairly large class of sets A.
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作者：MIKAMI, T
作者单位：Brown University
摘要：We consider the jump-type Markov processes which are small random perturbations of dynamical systems and their empirical processes. We prove large deviations theorems for empirical measures which are marginal measures of empirical processes at the exit time of Markov processes from a bounded domain in a d-dimensional Euclidean space R(d).
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作者：ROBERTS, GO
摘要：The problem of approximating boundary hitting times for diffusion processes, and in particular Brownian motion, is considered. Using a combination of probabilistic and function-analytic techniques, approximations for conditioned diffusion distributions are obtained. These lead to approximations for the distribution of the hitting time itself. The approximations are split into three cases depending on whether the boundary is upper case, approximation square root or lower case, and one-sided bou...
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作者：FREIDLIN, M
摘要：We consider single equations and systems of reaction-diffusion equations depending on small parameter. These equations are generalizations of the Kolmogorov-Petrovskii-Piskunov equation. Using the large deviation princple, we describe the asymptotic behavior of solutions.
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作者：ROSEN, J; YOR, M
作者单位：Sorbonne Universite
摘要：We develop explicit stochastic integral representations for the renormalized triple intersection local time of planar Brownian motion. Our representations involve a new type of double stochastic integral, the bilateral stochastic integral, which is developed in detail.
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作者：BLOUNT, D
摘要：Particles placed in N cells on the unit interval give birth or die according to linear rates. Adjacent cells are coupled by diffusion with a rate proportional to N2. Cell numbers are divided by a density parameter to represent concentrations, and the resulting space-time Markov process is compared to a corresponding deterministic model, the solution to a partial differential equation. The models are viewed as Hilbert space valued processes and compared by means of a law of large numbers and ce...
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作者：SCHURGER, K
作者单位：Australian National University
摘要：Based on two notions of almost subadditivity which were introduced by Derriennic and Schurger, two a.s. limit theorems are proved which both generalize Kingman's subadditive ergodic theorem. These results, being valid under weak moment conditions, are obtained by short proofs. One of these proofs is completely elementary and does not even make use of Birkhoff's ergodic theorem which, instead, is obtained as a by-product. Finally, an improvement of Liggett's a.s. limit theorem is given.
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作者：PEMANTLE, R
作者单位：Cornell University
摘要：Consider the nearest neighbor graph for the integer lattice Z(d) in d dimensions. For a large finite piece of it, consider choosing a spanning tree for that piece uniformly among all possible subgraphs that are spanning trees. As the piece gets larger, this approaches a limiting measure on the set of spanning graphs for Z(d). This is shown to be a tree if and only if d less-than-or-equal-to 4. In this case, the tree has only one topological end, that is, there are no doubly infinite paths. Whe...
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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：CARLEN, E; KREE, P
作者单位：Sorbonne Universite
摘要：For a continuous martingale M, let denote the increasing process. Let I0, I1,... denote the iterated stochastic integrals of M. We prove the inequalities of Burkholder-Davis-Gundy type, [GRAPHICS] where ln A(p,n) approximately ln B(p,n) approximately -(n/2)ln n as n --> infinity. Our proof requires the sharp constant b(p) in Burkholder-Davis-Gundy inequalities parallel-to M parallel-to p less-than-or-equal-to b(p) parallel-to 1/2 parallel-to p. In the Appendix we prove sup(p) greater-than-or-e...
