排序方式: 共有38条查询结果,搜索用时 15 毫秒
11.
Vincent Beffara Vladas Sidoravicius Maria Eulalia Vares 《Probability Theory and Related Fields》2010,147(3-4):565-581
We study a variant of poly-nuclear growth where the level boundaries perform continuous-time, discrete-space random walks, and study how its asymptotic behavior is affected by the presence of a columnar defect on the line. We prove that there is a non-trivial phase transition in the strength of the perturbation, above which the law of large numbers for the height function is modified. 相似文献
12.
Let α? (1,2) and X
α
be a symmetric α-stable (S α S) process with stationary increments given by the mixed moving average
where is a standard Lebesgue space, is some measurable function and M
α
is a SαS random measure on X ×ℝ with the control measure m
α
(dx, du) = μ(dx)du. We show that if X
α
is self-similar, then it is determined by a nonsingular flow, a related cocycle and a semi-additive functional. By using
the Hopf decomposition of the flow into its dissipative and conservative components, we establish a unique decomposition in
distribution of X
α
into two independent processes
where the process X
α
D
is determined by a nonsingular dissipative flow and the process X
α
C
is determined by a nonsingular conservative flow. In this decomposition, the linear fractional stable motion, for example,
is determined by a conservative flow.
Received: 20 June 2000 / Revised version: 6 September 2001 / Published online: 14 June 2002 相似文献
13.
Dilated Fractional Stable Motions 总被引:2,自引:0,他引:2
Dilated fractional stable motions are stable, self-similar, stationary increments random processes which are associated with dissipative flows. Self-similarity implies that their finite-dimensional distributions are invariant under scaling. In the Gaussian case, when the stability exponent equals 2, dilated fractional stable motions reduce to fractional Brownian motion. We suppose here that the stability exponent is less than 2. This implies that the dilated fractional stable motions have infinite variance and hence they cannot be characterised by a covariance function. These dilated fractional stable motions are defined through an integral representation involving a nonrandom kernel. This kernel plays a fundamental role. In this work, we study the space of kernels for which the dilated processes are well-defined, indicate connections to Sobolev spaces, discuss uniqueness questions and relate dilated fractional stable motions to other self-similar processes. We show that a number of processes that have been obtained in the literature, are in fact dilated fractional stable motions, for example, the telecom process obtained as limit of renewal reward processes, the Takenaka processes and the so-called random wavelet expansion processes. 相似文献
14.
Integration questions related to fractional Brownian motion 总被引:1,自引:0,他引:1
Let {B
H
(u)}
u
∈ℝ be a fractional Brownian motion (fBm) with index H∈(0, 1) and (B
H
) be the closure in L
2(Ω) of the span Sp(B
H
) of the increments of fBm B
H
. It is well-known that, when B
H
= B
1/2 is the usual Brownian motion (Bm), an element X∈(B
1/2) can be characterized by a unique function f
X
∈L
2(ℝ), in which case one writes X in an integral form as X = ∫ℝ
f
X
(u)dB
1/2(u). From a different, though equivalent, perspective, the space L
2(ℝ) forms a class of integrands for the integral on the real line with respect to Bm B
1/2. In this work we explore whether a similar characterization of elements of (B
H
) can be obtained when H∈ (0, 1/2) or H∈ (1/2, 1). Since it is natural to define the integral of an elementary function f = ∑
k
=1
n
f
k
1
[uk,uk+1)
by ∑
k
=1
n
f
k
(B
H
(u
k
+1) −B
H
(u
k
)), we want the spaces of integrands to contain elementary functions. These classes of integrands are inner product spaces.
If the space of integrands is not complete, then it characterizes only a strict subset of (B
H
). When 0<H<1/2, by using the moving average representation of fBm B
H
, we construct a complete space of integrands. When 1/2<H<1, however, an analogous construction leads to a space of integrands which is not complete. When 0<H<1/2 or 1/2<H<1, we also consider a number of other spaces of integrands. While smaller and henceincomplete, they form a natural choice
and are convenient to workwith. We compare these spaces of integrands to the reproducing kernel Hilbert space of fBm.
Received: 9 August 1999 / Revised version: 10 January 2000 / Published online: 18 September 2000 相似文献
15.
The problem of synthesizing multivariate stationary series Y[n]=(Y1[n],…,YP[n])T, n∈Z, with prescribed non-Gaussian marginal distributions, and a targeted covariance structure, is addressed. The focus is on constructions based on a memoryless transformation Yp[n]=fp(Xp[n]) of a multivariate stationary Gaussian series X[n]=(X1[n],…,XP[n])T. The mapping between the targeted covariance and that of the Gaussian series is expressed via Hermite expansions. The various choices of the transforms fp for a prescribed marginal distribution are discussed in a comprehensive manner. The interplay between the targeted marginal distributions, the choice of the transforms fp, and on the resulting reachability of the targeted covariance, is discussed theoretically and illustrated on examples. Also, an original practical procedure warranting positive definiteness for the transformed covariance at the price of approximating the targeted covariance is proposed, based on a simple and natural modification of the popular circulant matrix embedding technique. The applications of the proposed methodology are also discussed in the context of network traffic modeling. Matlab codes implementing the proposed synthesis procedure are publicly available at http://www.hermir.org. 相似文献
16.
Hannes Helgason Stefanos Kechagias Vladas Pipiras 《Journal of computational and graphical statistics》2016,25(4):1158-1175
Circulant matrix embedding is one of the most popular and efficient methods for the exact generation of Gaussian stationary univariate series. Although the idea of circulant matrix embedding has also been used for the generation of Gaussian stationary random fields, there are many practical covariance structures of random fields where classical embedding methods break down. In this work, we propose a novel methodology that adaptively constructs feasible circulant embeddings based on convex optimization with an objective function measuring the distance of the covariance embedding to the targeted covariance structure over the domain of interest. The optimal value of the objective function will be zero if and only if there exists a feasible embedding for the a priori chosen embedding size. 相似文献
17.
In this contribution, the statistical performance of the wavelet-based estimation procedure for the Hurst parameter is studied
for non-Gaussian long-range dependent processes obtained from point transformations of Gaussian processes. The statistical
properties of the wavelet coefficients and the estimation performance are compared both for processes having the same covariance
but different marginal distributions and for processes having the same covariance and same marginal distributions but obtained
from different point transformations, analyzed using mother wavelets with different number of vanishing moments. It is shown
that the reduction of the dependence range from long to short by increasing the number of vanishing moments, observed for
Gaussian processes, and at the origin of the popularity of the wavelet-based estimator, does not hold in general for non-Gaussian
processes. Crucially, it is also observed that the Hermite rank of the point transformation impacts significantly the statistical
properties of the wavelet coefficients and the estimation performance and also that processes having identical marginal distributions
and covariance function can yet yield significantly different estimation performance. These results are interpreted in the
light of central and noncentral limit theorems that are fundamental when dealing with long-range dependent processes. Moreover,
it will be shown that, on condition that estimation is performed using a range of scales restricted to the coarsest practically
available, an approximate, yet analytical and simple to use in practice, formula can be proposed for the evaluation of the
variance of the wavelet-based estimator of the Hurst parameter. 相似文献
18.
19.
It is known that Hermite processes have a finite-time interval representation. For fractional Brownian motion, the representation has been well known and plays a fundamental role in developing stochastic calculus for the process. For the Rosenblatt process, the finite-time interval representation was originally established by using cumulants. The representation was extended to general Hermite processes through the convergence of suitable partial sum processes. We provide here an alternative and different proof for the finite-time interval representation of Hermite processes. The approach is based on regularization of Hermite processes and the fractional Gaussian noises underlying them, and does not use cumulants nor convergence of partial sums. 相似文献
20.
We provide general conditions for normalized, time-scaled stochastic integrals of independently scattered, Lévy random measures
to converge to a limit. These integrals appear in many applied problems, for example, in connection to models for Internet
traffic, where both large scale and small scale asymptotics are considered. Our result is a handy tool for checking such convergence.
Numerous examples are provided as illustration. Somewhat surprisingly, there are examples where rescaling towards large times
scales yields a Gaussian limit and where rescaling towards small time scales yields an infinite variance stable limit, and
there are examples where the opposite occurs: a Gaussian limit appears when one converges towards small time scales and an
infinite variance stable limit occurs when one converges towards large time scales.
相似文献