首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 203 毫秒
1.
We study asymptotic behavior of the empirical conditional value-at-risk (CVaR). In particular, the Berry–Essen bound, the law of iterated logarithm, the moderate deviation principle and the large deviation principle for the empirical CVaR are obtained. We also give some numerical examples.  相似文献   

2.
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   

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.
We discuss the asymptotic behavior of weighted empirical processes of stationary linear random fields in with long-range dependence. It is shown that an appropriately standardized empirical process converges weakly in the uniform-topology to a degenerated process of the form fZ, where Z is a standard normal random variable and f is the marginal probability density of the underlying random field.  相似文献   

5.
We consider the large deviation principle for the empirical measure of a diffusion in Euclidean space, which was first established by Donsker and Varadhan. We employ a weak convergence approach and obtain a characterization for the rate function that is dual to the one obtained by Donsker and Varadhan, and which allows us to evaluate the variational form of the rate function for both reversible and nonreversible diffusions.  相似文献   

6.
We give new constants in Talagrand's concentration inequality for maxima of empirical processes. Our approach is based on the Herbst method. The improvement we get concerns the constant in the variance factor, which is the one conjectured by Massart.  相似文献   

7.
We prove a strong invariance principle for the two-parameter empirical process of stationary sequences under a new weak dependence assumption. We give several applications of our results.  相似文献   

8.
Summary Using self-similarity of Brownian motion and its representation as a product measure on a binary tree, we construct a random sequence of probability measures which converges to the distribution of the Brownian bridge. We establish a large deviation principle for random fields on a binary tree. This leads to a class of probability measures with a certain self-similarity property. The same construction can be carried out forC[0, 1]-valued processes and we can describe, for instance, aC[0, 1]-valued Ornstein-Uhlenbeck process as a large deviation of Brownian sheet.  相似文献   

9.
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   

10.
We prove a Freidlin-Wentzell large deviation principle for multi-dimensional stochastic differential equations with non-Lipschitz coefficients and apply it to the Brownian motion on the diffeomorphism group of the disc constructed recently by Airault, Malliavin and Thalmaier.  相似文献   

11.
This paper studies moderate deviation behaviors of the generalized method of moments and generalized empirical likelihood estimators for generalized estimating equations, where the number of equations can be larger than the number of unknown parameters. We consider two cases for the data generating probability measure: the model assumption and local contaminations or deviations from the model assumption. For both cases, we characterize the first-order terms of the moderate deviation error probabilities of these estimators. Our moderate deviation analysis complements the existing literature of the local asymptotic analysis and misspecification analysis for estimating equations, and is useful to evaluate power and robust properties of statistical tests for estimating equations which typically involve some estimators for nuisance parameters.  相似文献   

12.
We study the asymptotic behaviour of the empirical distribution function derived from a stationary marked point process when a convex sampling window is expanding without bounds in all directions. We consider a random field model which assumes that the marks and the points are independent and admits dependencies between the marks. The main result is the weak convergence of the empirical process under strong mixing conditions on both independent components of the model. Applying an approximation principle weak convergence can be also shown for appropriately weighted empirical process defined from a stationary d-dimensional germ-grain process with dependent grains.  相似文献   

13.
An expansion of large deviation probabilities for martingales is given, which extends the classical result due to Cramér to the case of martingale differences satisfying the conditional Bernstein condition. The upper bound of the range of validity and the remainder of our expansion is the same as in the Cramér result and therefore are optimal. Our result implies a moderate deviation principle for martingales.  相似文献   

14.
We prove a large deviation principle for flows associated to stochastic differential equations with non-Lipschitz coefficients. As an application we establish a Schilder Theorem for the Brownian motion on the group of diffeomorphisms of the circle.  相似文献   

15.
In the first part of this paper, we prove the uniqueness of the solutions of SPDEs with reflection, which was left open in the paper [C. Donati-Martin, E. Pardoux, White noise driven SPDEs with reflection, Probab. Theory Related Fields 95 (1993) 1–24]. We also obtain the existence of the solution for more general coefficients depending on the past with a much shorter proof. In the second part of the paper, we establish a large deviation principle for SPDEs with reflection. The weak convergence approach is proven to be very efficient on this occasion.  相似文献   

16.
The paper provides a recursive interpretation for the technique known as bracketing with adaptive truncation. By way of illustration, a simple bound is derived for the expected value of the supremum of an empirical process, thereby leading to a simpler derivation of a functional central limit theorem due to Ossiander. The recursive method is also abstracted into a framework that consists of only a small number of assumptions about processes and functionals indexed by sets of functions. In particular, the details of the underlying probability model are condensed into a single inequality involving finite sets of functions. A functional central limit theorem of Doukhan, Massart and Rio, for empirical processes defined by absolutely regular sequences, motivates the generalization.  相似文献   

17.
A large deviation principle is derived for a class of stochastic reaction-diffusion partial differential equations with slow-fast components. The result shows that the rate function is exactly that of the averaged equation plus the fluctuating deviation which is a stochastic partial differential equation with small Gaussian perturbation. This result also confirms the effectiveness of the approximation of the averaged equation plus the fluctuating deviation to the slow-fast stochastic partial differential equations.  相似文献   

18.
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   

19.
Ito's rule is established for the diffusion processes on the graphs. We also consider a family of diffusions processes with small noise on a graph. Large deviation principle is proved for these diffusion processes and their local times at the vertices. Received: 12 February 1997 / Revised version: 3 March 1999  相似文献   

20.
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   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号