共查询到20条相似文献,搜索用时 15 毫秒
1.
Michel Mandjes Petteri Mannersalo Ilkka Norros Miranda van Uitert 《Stochastic Processes and their Applications》2006
Consider events of the form {Zs≥ζ(s),s∈S}, where Z is a continuous Gaussian process with stationary increments, ζ is a function that belongs to the reproducing kernel Hilbert space R of process Z, and S⊂R is compact. The main problem considered in this paper is identifying the function β∗∈R satisfying β∗(s)≥ζ(s) on S and having minimal R-norm. The smoothness (mean square differentiability) of Z turns out to have a crucial impact on the structure of the solution. As examples, we obtain the explicit solutions when ζ(s)=s for s∈[0,1] and Z is either a fractional Brownian motion or an integrated Ornstein–Uhlenbeck process. 相似文献
2.
Shui Feng 《Probability Theory and Related Fields》1994,100(2):227-252
Summary An N-particle system with mean field interaction is considered. The large deviation estimates for the empirical distributions as N goes to infinity are obtained under conditions which are satisfied, by many interesting models including the first and the second Schlögl models.Supported partially by a scholarship from the Faculty of Graduate Studies and Research of Carleton University and the NSERC operating grant of D.A. Dawson 相似文献
3.
Summary We study the asymptotic behaviour of asymmetrical spin glass dynamics in a Sherrington-Kirkpatrick model as proposed by Sompolinsky-Zippelius. We prove that the annealed law of the empirical measure on path space of these dynamics satisfy a large deviation principle in the high temperature regime. We study the rate function of this large deviation principle and prove that it achieves its minimum value at a unique probability measureQ which is not markovian. We deduce that the quenched law of the empirical measure converges to
Q
. Extending then the preceeding results to replicated dynamics, we investigate the quenched behavior of a single spin. We get quenched convergence toQ in the case of a symmetric initial law and even potential for the free spin. 相似文献
4.
Timo Seppäläinen 《Probability Theory and Related Fields》1998,112(2):221-244
We prove a large deviation principle with explicit rate functions for the length of the longest increasing sequence among
Poisson points on the plane. The rate function for lower tail deviations is derived from a 1977 result of Logan and Shepp
about Young diagrams of random permutations. For the upper tail we use a coupling with Hammersley's particle process and convex-analytic
techniques. Along the way we obtain the rate function for the lower tail of a tagged particle in a totally asymmetric Hammersley's
process.
Received: 22 July 1997 / Revised version: 23 March 1998 相似文献
5.
Masatake Hirao 《Statistics & probability letters》2011,81(11):1561-1564
Using the heat kernel estimates by Davies (1989) and Anker et al. (1996), we show large deviations for the radial processes of the Brownian motions on hyperbolic spaces. 相似文献
6.
7.
Hans-Otto Georgii 《Probability Theory and Related Fields》1994,99(2):171-195
Summary For Gibbsian systems of particles inR
d
, we investigate large deviations of the translation invariant empirical fields in increasing boxes. The particle interaction is given by a superstable, regular pair potential. The large deviation principle is established for systems with free or periodic boundary conditions and, under a stronger stability hypothesis on the potential, for systems with tempered boundary conditions, and for tempered (infinite-volume) Gibbs measures. As a by-product we obtain the Gibbs variational formula for the pressure. We also prove the asymptotic equivalence of microcanonical and grand canonical Gibbs distributions and establish a variational expression for the thermodynamic entropy density. 相似文献
8.
Yuri V. Borovskikh 《Journal of multivariate analysis》2008,99(8):1793-1806
We develop large deviation results with Cramér’s series and the best possible remainder term for bootstrapped U-statistics with non-degenerate bounded kernels. The method of the proof is based on the contraction technique of Keener, Robinson and Weber [R.W. Keener, J. Robinson, N.C. Weber, Tail probability approximations for U-statistics, Statist. Probab. Lett. 37 (1) (1998) 59-65], which is a natural generalization of the classical conjugate distribution technique due to Cramér [H. Cramér, Sur un nouveau théoréme-limite de la theorie des probabilites, Actual. Sci. Indust. 736 (1938) 5-23]. 相似文献
9.
This paper aims to derive large deviations for statistics of the Jacobi process already conjectured by M. Zani in her thesis. To proceed, we write in a simpler way the Jacobi semi-group density. Being given by a bilinear sum involving Jacobi polynomials, it differs from Hermite and Laguerre cases by the quadratic form of its eigenvalues. Our attempt relies on subordinating the process using a suitable random time change. This gives a Mehler-type formula whence we recover the desired semi-group density. Once we do, an adaptation of Zani’s result [M. Zani, Large deviations for squared radial Ornstein–Uhlenbeck processes, Stochastic. Process. Appl. 102 (1) (2002) 25–42] to the non-steep case will provide the required large deviations principle. 相似文献
10.
Terence Chan 《Probability Theory and Related Fields》1993,97(1-2):179-193
Summary This paper studies the large deviations of the empirical measure associated withn independent random variables with a degenerate limiting distribution asn. A large deviations principle — quite unlike the classical Sanov type results — is established for such empirical measures in a general Polish space setting. This result is applied to the large deviations for the empirical process of a system of interacting particles, in which the diffusion coefficient vanishes as the number of particles tends to infinity. A second way in which the present example differs from previous work on similar weakly interacting systems is that there is a singularity in the mean-field type interaction. 相似文献
11.
Dmitrii S. Silvestrov 《Acta Appl Math》1994,34(1-2):109-124
Coupling procedures for Markov renewal processes are described. Applications to ergodic theorems for processes with semi-Markov switchings are considered.This paper was partly prepared with the support of NFR Grant F-UP 10257-300. 相似文献
12.
A Boussinesq model for the Bénard convection under random influences is considered as a system of stochastic partial differential equations. This is a coupled system of stochastic Navier–Stokes equations and the transport equation for temperature. Large deviations are proved, using a weak convergence approach based on a variational representation of functionals of infinite-dimensional Brownian motion. 相似文献
13.
Summary We obtain large deviation estimates for the empirical measure of a class of interacting particle systems. These consist of a superposition of Glauber and Kawasaki dynamics and are described, in the hydrodynamic limit, by a reaction diffusion equation. We extend results of Kipnis, Olla and Varadhan for the symmetric exclusion process, and provide an approximation scheme for the rate functional. Some physical implications of our results are briefly indicated. 相似文献
14.
Timo Seppäläinen 《Probability Theory and Related Fields》1993,96(2):241-260
Summary We prove large deviation theorems for empirical measures of independent random fields whose distributions depend measurably on an auxiliary parameter. This dependence respects the action of the shift group, and a large deviation principle holds whenever a certain ergodicity condition is satisfied. We also investigate the entropy functions for these processes, especially in relation to the usual relative entropy. 相似文献
15.
We consider the standard first-passage percolation in Zd for d≥2 and we denote by ?nd−1,h(n) the maximal flow through the cylinder ]0,n]d−1×]0,h(n)] from its bottom to its top. Kesten proved a law of large numbers for the maximal flow in dimension 3: under some assumptions, ?nd−1,h(n)/nd−1 converges towards a constant ν. We look now at the probability that ?nd−1,h(n)/nd−1 is greater than ν+ε for some ε>0, and we show under some assumptions that this probability decays exponentially fast with the volume nd−1h(n) of the cylinder. Moreover, we prove a large deviation principle for the sequence (?nd−1,h(n)/nd−1,n∈N). 相似文献
16.
17.
Shulan Hu 《Stochastic Processes and their Applications》2011,121(1):61-90
In this paper, we prove the large deviation principle (LDP) for the occupation measures of not necessarily irreducible random dynamical systems driven by Markov processes. The LDP for not necessarily irreducible dynamical systems driven by i.i.d. sequence is derived. As a further application we establish the LDP for extended hidden Markov models, filling a gap in the literature, and obtain large deviation estimations for the log-likelihood process and maximum likelihood estimator of hidden Markov models. 相似文献
18.
19.
Lothar Heinrich 《Monatshefte für Mathematik》1997,124(3):237-253
We determine the exact rate of Poisson approximation and give a second-order Poisson-Charlier expansion for the number of excedances of a given levelL
n
among the firstn digits of inhomogeneousf-expansions of real numbers in the unit interval. The application of this general result to homogeneousf-expansions and, in particular, to regular continued fraction expansions provides not only a generalization but also a strengthening of a classical Poisson limit theorem due to W. Doeblin. 相似文献
20.
Summary A second order error bound is obtained for approximating h d
by h d
, where
is a convolution of measures andQ a compound Poisson measure on a measurable abelian group, and the functionh is not necessarily bounded. This error bound is more refined than the usual total variation bound in the sense that it contains the functionh. The method used is inspired by Stein's method and hinges on bounding Radon-Nikodym derivatives related to
. The approximation theorem is then applied to obtain a large deviation result on groups, which in turn is applied to multivariate Poisson approximation.Research of the second author was supported by Schweizerischer Nationalfonds 相似文献