共查询到20条相似文献,搜索用时 280 毫秒
1.
Antoine Lejay 《Probability Theory and Related Fields》2001,120(2):255-276
The probabilistic machinery (Central Limit Theorem, Feynman-Kac formula and Girsanov Theorem) is used to study the homogenization
property for PDE with second-order partial differential operator in divergence-form whose coefficients are stationary, ergodic
random fields. Furthermore, we use the theory of Dirichlet forms, so that the only conditions required on the coefficients
are non-degeneracy and boundedness.
Received: 27 August 1999 / Revised version: 27 October 2000 / Published online: 26 April 2001 相似文献
2.
Summary. We prove a functional central limit theorem for stationary random sequences given by the transformations
on the two-dimensional torus. This result is based on a functional central limit theorem for ergodic stationary martingale
differences with values in a separable Hilbert space of square integrable functions.
Received: 11 March 1997 / In revised form: 1 December 1997This research was supported by the Deutsche Forschungsgemeinschaft
and the Russian Foundation for Basic Research, grant 96-01-00096. The second author was also partially supported by INTAS,
grant 94-4194. 相似文献
3.
We consider a stationary grain model Ξ in ℝ
d
with convex, compact and smoothly bounded grains. We study the spherical contact distribution function F of Ξ and derive (under suitable assumptions) an explicit formula for its second derivative F″. The value F″(0) is of a simple form and admits a clear geometric interpretation.For the Boolean model we obtain an interesting new formula
for the(d− 1)-st quermass density.
Received: 22 November 1999 / Revised version: 2 November 2000 /?Published online: 14 June 2001 相似文献
4.
Zvi Artstein 《Probability Theory and Related Fields》2001,120(3):369-394
The collection of sub-σ-fields of a Borel measure space when endowed with the topology of strong convergence is in general
not a compact space. The paper offers a completion of this space which makes it compact. The elements which are added to the
space are called relaxed σ-fields. A notion of relaxed conditional expectation with respect to a relaxed σ-field is identified.
The relaxed conditional expectation is a probability measure-valued map. It is shown that the conditional expectation operator
is continuous on the completion of the space. Other properties of conditional expectation are lifted to and interpreted in
the relaxed framework.
Received: 22 February 1999 / Revised version: 23 October 2000 / Published online: 8 May 2001 相似文献
5.
Emmanuel Rio 《Probability Theory and Related Fields》2001,119(2):163-175
We propose new concentration inequalities for maxima of set-indexed empirical processes. Our approach is based either on
entropy inequalities or on martingale methods. The improvements we get concern the rate function which is exactly the large
deviations rate function of a binomial law in most of the cases.
Received: 11 January 2000 / Revised version: 12 May 2000 / Published online: 14 December 2000 相似文献
6.
We consider the almost sure asymptotic behavior of the periodogram of stationary and ergodic sequences. Under mild conditions we establish that the limsup of the periodogram properly normalized identifies almost surely the spectral density function associated with the stationary process. Results for a specified frequency are also given. Our results also lead to the law of the iterated logarithm for the real and imaginary parts of the discrete Fourier transform. The proofs rely on martingale approximations combined with results from harmonic analysis and techniques from ergodic theory. Several applications to linear processes and their functionals, iterated random functions, mixing structures and Markov chains are also presented. 相似文献
7.
This paper is part of our efforts to develop Stein's method beyond uniform bounds in normal approximation. Our main result
is a proof for a non-uniform Berry–Esseen bound for independent and not necessarily identically distributed random variables
without assuming the existence of third moments. It is proved by combining truncation with Stein's method and by taking the
concentration inequality approach, improved and adapted for non-uniform bounds. To illustrate the technique, we give a proof
for a uniform Berry–Esseen bound without assuming the existence of third moments.
Received: 2 March 2000 / Revised version: 20 July 2000 / Published online: 26 April 2001 相似文献
8.
We consider the flow of a stochastic differential equation on d-dimensional Euclidean space. We show that if the Lie algebra generated by its diffusion vector fields is finite dimensional
and solvable, then the flow is conjugate to the flow of a non-autonomous random differential equation, i.e. one can be transformed
into the other via a random diffeomorphism of d-dimensional Euclidean space. Viewing a stochastic differential equation in this form which appears closer to the setting
of ergodic theory, can be an advantage when dealing with asymptotic properties of the system. To illustrate this, we give
sufficient criteria for the existence of global random attractors in terms of the random differential equation, which are
applied in the case of the Duffing-van der Pol oscillator with two independent sources of noise.
Received: 25 May 1999 / Revised version: 19 October 2000 / Published online: 26 April 2001 相似文献
9.
10.
Multiple fractional integrals 总被引:2,自引:0,他引:2
Multiple integrals with respect to fractional Brownian motion (with H > 1/2) are constructed for a large class of functions. The first and second moments of the multiple integrals are explicitly
identified.
Received: 23 February 1998 / Revised version: 31 July 1998 相似文献
11.
Peter Mörters 《Probability Theory and Related Fields》2000,118(1):49-64
The Kallianpur–Robbins law describes the long term asymptotic behaviour of integrable additive functionals of Brownian motion
in the plane. In this paper we prove an almost sure version of this result. It turns out that, differently from many known
results, this requires an iterated logarithmic average. A similar result is obtained for the small scales asymptotic by means
of an ergodic theorem of Chacon–Ornstein type, which allows an exceptional set of scales.
Received: 8 May 1998 / Revised version: 1 December 1999 / Published online: 8 August 2000 相似文献
12.
M.S. Bernabei 《Probability Theory and Related Fields》2001,119(3):410-432
The Central Limit Theorem for a model of discrete-time random walks on the lattice ℤν in a fluctuating random environment was proved for almost-all realizations of the space-time nvironment, for all ν > 1 in
[BMP1] and for all ν≥ 1 in [BBMP]. In [BMP1] it was proved that the random correction to the average of the random walk for
ν≥ 3 is finite. In the present paper we consider the cases ν = 1,2 and prove the Central Limit Theorem as T→∞ for the random correction to the first two cumulants. The rescaling factor for theaverage is for ν = 1 and (ln T), for ν=2; for the covariance it is , ν = 1,2.
Received: 25 November 1999 / Revised version: 7 June 2000 / Published online: 15 February 2001 相似文献
13.
The main result in this paper states that if a one-parameter Gaussian process has C
2k
paths and satisfies a non-degeneracy condition, then the distribution of its maximum on a compact interval is of class C
k
. The methods leading to this theorem permit also to give bounds on the successive derivatives of the distribution of the
maximum and to study their asymptotic behaviour as the level tends to infinity.
Received: 14 May 1999 / Revised version: 18 October 1999 / Published online: 14 December 2000 相似文献
14.
We consider the distributions of the lengths of the longest weakly increasing and strongly decreasing subsequences in words
of length N from an alphabet of k letters. (In the limit as k→∞ these become the corresponding distributions for permutations on N letters.) We find Toeplitz determinant representations for the exponential generating functions (on N) of these distribution functions and show that they are expressible in terms of solutions of Painlevé V equations. We show
further that in the weakly increasing case the generating unction gives the distribution of the smallest eigenvalue in the
k×k Laguerre random matrix ensemble and that the distribution itself has, after centering and normalizing, an N→∞ limit which is equal to the distribution function for the largest eigenvalue in the Gaussian Unitary Ensemble of k×k hermitian matrices of trace zero.
Received: 9 September 1999 / Revised version: 24 May 2000 / Published online: 24 January 2001 相似文献
15.
Nathanaël Enriquez Jacques Franchi Yves Le Jan 《Probability Theory and Related Fields》2001,119(2):213-255
Let ℳ be a geometrically finite hyperbolic surface with infinite volume, having at least one cusp. We obtain the limit law
under the Patterson-Sullivan measure on T
1ℳ of the windings of the geodesics of ℳ around the cusps. This limit law is stable with parameter 2δ− 1, where δ is the Hausdorff
dimension of the limit set of the subgroup Γ of M?bius isometries associated with ℳ. The normalization is t
−1/(2δ−1), for geodesics of length t. Our method relies on a precise comparison between geodesics and diffusion paths, for which we need to approach the Patterson-Sullivan
measure mentioned above by measures that are regular along the stable leaves.
Received: 8 October 1999 / Revised version: 2 June 2000 / Published online: 21 December 2000 相似文献
16.
We establish a connection between the structure of a stationary symmetric α-stable random field (0<α<2) and ergodic theory of non-singular group actions, elaborating on a previous work by Rosiński (Ann. Probab. 28:1797–1813,
2000). With the help of this connection, we study the extreme values of the field over increasing boxes. Depending on the ergodic
theoretical and group theoretical structures of the underlying action, we observe different kinds of asymptotic behavior of
this sequence of extreme values.
Supported in part by NSF grant DMS-0303493, NSA grant MSPF-05G-049 and NSF training grant “Graduate and Postdoctoral Training
in Probability and Its Applications” at Cornell University. 相似文献
17.
Many interacting particle systems with short range interactions are not ergodic, but converge weakly towards a mixture of
their ergodic invariant measures. The question arises whether a.s.the process eventually stays close to one of these ergodic
states, or if it changes between the attainable ergodic states infinitely often (“recurrence”). Under the assumption that
there exists a convergence–determining class of distributions that is (strongly) preserved under the dynamics, we show that
the system is in fact recurrent in the above sense.
We apply our method to several interacting particle systems, obtaining new or improved recurrence results. In addition, we
answer a question raised by Ed Perkins concerning the change of the locally predominant type in a model of mutually catalytic
branching.
Received: 22 January 1999 / Revised version: 24 May 1999 相似文献
18.
Chaos decomposition of multiple integrals with respect to fractional Brownian motion (with H > 1/2) is given. Conversely the chaos components are expressed in terms of the multiple fractional integrals. Tensor product
integrals are introduced and series expansions in those are considered. Strong laws for fractional Brownian motion are proved
as an application of multiple fractional integrals.
Received: 22 September 1998 / Revised version: 20 April 1999 相似文献
19.
20.
Let (M
t
) be any martingale with M
0≡ 0, an intermediate law M
1∼μ1, and terminal law M
2∼μ2, and let Mˉ
2≡ sup0≤
t
≤2
M
t
. In this paper we prove that there exists an upper bound, with respect to stochastic ordering of probability measures, on
the law of Mˉ
2. We construct, using excursion theory, a martingale which attains this maximum. Finally we apply this result to the robust
hedging of a lookback option.
Received: 26 December 1998 / Revised version: 20 April 2000 /?Published online: 15 February 2001 相似文献