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11.
The multifractional Brownian motion (MBM) processes are locally self-similar Gaussian processes. They extend the classical fractional Brownian motion processes BH={BH(t)}t∈R by allowing their self-similarity parameter H∈(0,1) to depend on time. 相似文献
12.
13.
Estimating the Heavy Tail Index from Scaling Properties 总被引:4,自引:0,他引:4
This paper deals with the estimation of the tail index for empirical heavy-tailed distributions, such as have been encountered in telecommunication systems. We present a method (called the scaling estimator) based on the scaling properties of sums of heavy-tailed random variables. It has the advantages of being nonparametric, of being easy to apply, of yielding a single value, and of being relatively accurate on synthetic datasets. Since the method relies on the scaling of sums, it measures a property that is often one of the most important effects of heavy-tailed behavior. Most importantly, we present evidence that the scaling estimator appears to increase in accuracy as the size of the dataset grows. It is thus particularly suited for large datasets, as are increasingly encountered in measurements of telecommunications and computing systems. 相似文献
14.
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
15.
We construct two new classes of symmetric stable self-similar random fields with stationary increments, one of the moving average type, the other of the harmonizable type. The fields are defined through an integral representation whose kernel involves a norm on
n
. We examine how the choice of the norm affects the finite-dimensional distributions. We also study the processes which are obtained by projecting the random fields on a one-dimensional subspace. We compare these projection processes with each other and with other well-known self-similar processes and we characterize their asymptotic dependence structure.The research was done at Boston University while the first author was on leave from the Hugo Steinhaus Center, Poland. The second author was partially supported by the ONR Grant N00014-90-J-1287 at Boston University and by a grant of the United States-Israel Binational Science Foundation. 相似文献
16.
Convergence of integrated processes of arbitrary Hermite rank 总被引:5,自引:0,他引:5
Murad S. Taqqu 《Probability Theory and Related Fields》1979,50(1):53-83
Summary Let {X(s), –<s<} be a normalized stationary Gaussian process with a long-range correlation. The weak limit in C[0,1] of the integrated process
, is investigated. Here d(x) = x
H
L(x) with
<H<1 and L(x) is a slowly varying function at infinity. The function G satisfies EG(X(s))=0, EG
2
(X(s))< and has arbitrary Hermite rank m1. (The Hermite rank of G is the index of the first non-zero coefficient in the expansion of G in Hermite polynomials.) It is shown thatZ
x
(t) converges for all m1 to some process ¯Z
m
(t) that depends essentially on m. The limiting process ¯Z
m
(t) is characterized through various representations involving multiple Itô integrals. These representations are all equivalent in the finite-dimensional distributions sense. The processes ¯Z
m
(t) are non-Gaussian when m2. They are self-similar, that is,¯Z
m
(at) and a
H
¯Z
m
(t) have the same finite-dimensional distributions for all a>0.Research supported by the National Science Foundation grants MCS 77-03543 and ENG 78-11454.This paper contains results closely connected to those of the paper by Dobrushin and Major, Z. Wahrscheinlichkeitstheorie verw. Gebiete 50, 27–52 (1979). The investigations were done independently and at about the same time. Different methods were usedDedicated to Professor Leopold Schmetterer on occasion of his 60th Birthday 相似文献
17.
18.
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
19.
R. Pohl H. Daniel F. J. Hartmann P. Hauser Y. W. Liu F. Kottmann C. Maierl V. E. Markushin M. Mühlbauer C. Petitjean W. Schott D. Taqqu 《Hyperfine Interactions》2001,138(1-4):35-40
Kinetic energy distributions of muonic hydrogen atoms μp(1S) have been obtained by means of a time-of-flight technique for
hydrogen gas pressures between 4 and 64 hPa. A high energy component of ∼900 eV observed in the data is interpreted as the
signature of long-lived μp(2S) atoms, which are quenched in a non-radiative process leading to the observed high energy: the
collision of a thermalized μp(2S) atom with a hydrogen molecule H2 results in the resonant formation of a {[(ppμ)+]*pee}* molecule. Then the (ppμ)+ complex undergoes Coulomb de-excitation and the ∼1.9 keV excitation energy is shared between a μp(1S) atom and one proton.
The preliminary analysis of the time spectra gives a long-lived μp(2S) population of ∼1% of all stopped muons, and a quenching
rate of ∼4⋅1011 s−1.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
20.
F. Kottmann W. Amir F. Biraben C. A. N. Conde S. Dhawan T. W. Hänsch F. J. Hartmann V. W. Hughes O. Huot P. Indelicato L. Julien P. Knowles S. Kazamias Y.-W. Liu F. Mulhauser F. Nez R. Pohl P. Rabinowitz J. M. F. dos Santos L. A. Schaller H. Schneuwly W. Schott D. Taqqu J. F. C. A. Veloso 《Hyperfine Interactions》2001,138(1-4):55-60
A measurement of the 2S Lamb shift in muonic hydrogen (μ−p) is being prepared at the Paul Scherrer Institute (PSI). The goal of the experiment is to measure the energy difference
ΔE(25
P
3/2−23
S
1/2) by laser spectroscopy (λ≈6μm) to a precision of 30 ppm and to deduce the root mean square (rms) proton charge radius with
10−3 relative accuracy, 20 times more precise than presently known.
An important prerequisite to this experiment is the availability of long-lived μp2S
-atoms. A 2S-lifetime of ∼1 μs – sufficiently long to perform the laser experiment – at H2 gas pressures of 1–2 hPa was deduced from recent measurements of the collisional 2S-quenching rate. A new low-energy negative muon beam yields an order of magnitude more muon stops in a small low-density gas
volume than a conventional cloud muon beam. A stack of ultra-thin carbon foils is the key element of a fast detector for keV-muons.
The development of a 2 keV X-ray detector and a 3-stage laser system providing 0.5 mJ laser pulses at 6 μm is on the way.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献