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作者：CHENG, ZM; LEBOWITZ, JL; MAJOR, P
作者单位：Rutgers University System; Rutgers University New Brunswick; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences
摘要：Let A be an oval with a nice boundary in R2, R a large positive number, c > 0 some fixed number and alpha a uniformly distributed random vector in the unit square [0, 1]2. We are interested in the number of lattice points in the shifted annular region consisting of the difference of the sets {(R + c/R) A - alpha} and {(R - c/R) A - alpha}. We prove that when R tends to infinity, the expectation and the variance of this random variable tend to 4c times the area of the set A, i.e. to the area of...
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作者：PESZAT, S
摘要：The large deviation principle obtained by Freidlin and Wentzell for measures associated with finite-dimensional diffusions is extended to measures given by stochastic evolution equations with non-additive random perturbations. The proof of the main result is adopted from the Priouret paper concerning finite-dimensional diffusions. Exponential tail estimates for infinite-dimensional stochastic convolutions are used as main tools.
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作者：CARMONA, P; PETIT, F; YOR, M
摘要：The scaling property of Brownian motion is exploited systematically in order to extend Paul Levy's are sine law to Brownian motion perturbed by its local time at 0. Other important ingredients of the proofs are some Ray-Knight theorems for local times.
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作者：ALBEVERIO, S; MOLCHANOV, SA; SURGAILIS, D
作者单位：Vilnius University; University of North Carolina; University of North Carolina Charlotte
摘要：The model of the potential turbulence described by the 3-dimensional Burgers' equation with random initial data was developped by Zeldovich and Shandarin, in order to explain the existing Large Scale Structure of the Universe. Most of the recent probabilistic investigations of large time asymptotics of the solution deal with the central limit type results (the ''Gaussian scenario''), under suitable moment assumptions on the initial velocity field. These results and some open questions are disc...
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作者：HOHNLE, R; STURM, KT
作者单位：University of Erlangen Nuremberg
摘要：Let (X(t), P-x) be an m-symmetric Markov process with a strictly transition density. Consider the additive functional A(t):= integral(0)(t)f(X(s)) (is where f: E --> [0, infinity] is a universally measurable function on the state space E. Among others, we prove that P-x(A(t) < infinity) = 1, for some x is an element of EE and some t > 0, already implies P-x(A(t) < infinity) = 1, for quasi every x is an element of E and all t > 0. The latter is also equivalent to P-x(A(t) < infinity) > 0, for q...
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作者：LI, XM
摘要：Here we discuss the regularity of solutions of SDE's and obtain conditions under which a SDE on a complete Riemannian manifold M has a global smooth solution flow, in particular improving the usual global Lipschitz hypothesis when M = R(n). There are also results on non-explosion of diffusions.
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作者：USTUNEL, AS; ZAKAI, M
作者单位：Technion Israel Institute of Technology
摘要：In this paper we study some classes of Wiener functionals whose elements can be composed with a non-linear, non-absolutely continous transformation of the form of perturbation of identity in the direction of Cameron-Martin space, We show that under certain conditions the image of the Wiener measure under the above transformation induces a generalized Wiener functional on certain Sobolev spaces generalizing the Radon-Nikodym relation to non absolutely continuous transformations. A series repres...
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作者：CRAUEL, H; FLANDOLI, F
作者单位：Scuola Normale Superiore di Pisa
摘要：A criterion for existence of global random attractors for RDS is established. Existence of invariant Markov measures supported by the random attractor is proved. For SPDE this yields invariant measures for the associated Markov semigroup. The results are applied to reaction diffusion equations with additive white noise and to Navier-Stokes equations with multiplicative and with additive white noise.
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作者：HALL, P; PATIL, P
作者单位：Australian National University
摘要：We introduce nonparametric estimators of the autocovariance of a stationary random field. One of our estimators has the property that it is itself an autocovariance. This feature enables the estimator to be used as the basis of simulation studies such as those which are necessary when constructing bootstrap confidence intervals for unknown parameters. Unlike estimators proposed recently by other authors, our own do not require assumptions such as isotropy or monotonicity. Indeed, like nonparam...
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作者：CSAKI, E; FOLDES, A; REVESZ, P
作者单位：City University of New York (CUNY) System; Technische Universitat Wien
摘要：Let S1, S2,... be a sequence of sums of i.i.d. random variables. The properties of the logarithmic average [GRAPHICS] will be studied under some conditions
