共查询到20条相似文献,搜索用时 15 毫秒
1.
Norbert Patzschke 《Monatshefte für Mathematik》2004,142(3):243-266
We show that the tangent measure distribution of a self-conformal measure exists at almost all points of the support of the measure. Moreover, we prove, that it is the same for almost all points. 相似文献
2.
Toshiro Watanabe 《Probability Theory and Related Fields》2000,117(3):387-405
P.S. numbers are introduced in relation to absolute continuity of some infinite Bernoulli convolutions. Absolute continuity
and continuous singularity of some semi-selfdecomposable distributions are studied as marginal distributions of subordinators.
It is shown that these properties are widely different according as their spans are P.V. numbers or the reciprocals of P.S.
numbers. A simple example of a subordinator whose distribution is continuous singular for small time and absolutely continuous
for large time is given. Absolute continuity of convolutions of multidimensional homogeneous self-similar measures are also
discussed.
Received: 27 December 1998 / Revised version: 20 August 1999 / Published online: 31 May 2000 相似文献
3.
Jean-François Delmas 《Probability Theory and Related Fields》1999,114(4):505-547
We consider a super-Brownian motion X. Its canonical measures can be studied through the path-valued process called the Brownian snake. We obtain the limiting
behavior of the volume of the ɛ-neighborhood for the range of the Brownian snake, and as a consequence we derive the analogous
result for the range of super-Brownian motion and for the support of the integrated super-Brownian excursion. Then we prove
the support of X
t
is capacity-equivalent to [0, 1]2 in ℝd, d≥ 3, and the range of X, as well as the support of the integrated super-Brownian excursion are capacity-equivalent to [0, 1]4 in ℝd, d≥ 5.
Received: 7 April 1998 / Revised version: 2 October 1998 相似文献
4.
Tangent measure distributions were introduced byBandt [2] andGraf [8] as a means to describe the local geometry of self-similar sets generated by iteration of contractive similitudes. In this paper we study the tangent measure distributions of hyperbolic Cantor sets generated by certain contractive mappings, which are not necessarily similitudes. We show that the tangent measure distributions of these sets equipped with either Hausdorff- or Gibbs measure are unique almost everywhere and give an explicit formula describing them as probability distributions on the set of limit models ofBedford andFisher [5]. 相似文献
5.
In this paper we present a martingale related to the exit measures of super Brownian motion. By changing measure with this
martingale in the canonical way we have a new process associated with the conditioned exit measure. This measure is shown
to be identical to a measure generated by a non-homogeneous branching particle system with immigration of mass. An application
is given to the problem of conditioning the exit measure to hit a number of specified points on the boundary of a domain.
The results are similar in flavor to the “immortal particle” picture of conditioned super Brownian motion but more general,
as the change of measure is given by a martingale which need not arise from a single harmonic function.
Received: 27 August 1998 / Revised version: 8 January 1999 相似文献
6.
Stéphane Jaffard 《Probability Theory and Related Fields》1999,114(2):207-227
We show that the sample paths of most Lévy processes are multifractal functions and we determine their spectrum of singularities.
Received: 21 February 1997 / Revised version: 27 July 1998 相似文献
7.
Scaling properties of Hausdorff and packing measures 总被引:1,自引:0,他引:1
Let . Let be a continuous increasing function defined on , for which and is a decreasing function of t. Let be a norm on , and let , , denote the corresponding metric, and Hausdorff and packing measures, respectively. We characterize those functions such that the corresponding Hausdorff or packing measure scales with exponent by showing it must be of the form , where L is slowly varying. We also show that for continuous increasing functions and defined on , for which , is either trivially true or false: we show that if , then for a constant c, where is the Lebesgue measure on . Received June 17, 2000 / Accepted September 6, 2000 / Published online March 12, 2001 相似文献
8.
For q ≥ 0, Olsen [1] has attained the exact rate of convergence of the L
q
-spectrum of a self-similar measure and showed that the so-called empirical multifractal moment measures converges weakly
to the normalized multifractal measures. Unfortunately, nothing is known for q < 0. Indeed, the problem of analysing the L
q
- spectrum for q < 0 is generally considered significantly more difficult since the L
q
-spectrum is extremely sensitive to small variations of μ for q < 0. In [2] we showed that self-similar measures satisfying the Open Set Condition (OSC) are Ahlfors regular and, using this
fact, we obtained the exact rate of convergence of the L
q
-spectrum of a self-similar measure satisfying the OSC for q < 0. In this paper, we apply the results from [2] to show the empirical multifractal q’th moment measures of self-similar
measures satisfying the OSC converges weakly to the normalized multifractal Hausdorff measures for q < 0.
Authors’ addresses: Jiaqing Xiao, School of Science, Wuhan University of Technology, Wuhan 430070, China; Wu Min, School of
Mathematical Sciences, South China University of Technology, Guangzhou, 510640, China 相似文献
9.
Summary. A super-Brownian motion in with “hyperbolic” branching rate , is constructed, which symbolically could be described by the formal stochastic equation (with a space-time white noise ). Starting at
this superprocess will never hit the catalytic center: There is an increasing sequence of Brownian stopping times strictly smaller than the hitting time of such that with probability one Dynkin's stopped measures vanish except for finitely many
Received: 27 November 1995 / In revised form: 24 July 1996 相似文献
10.
Let ? be the genealogical tree of a supercritical multitype Galton–Watson process, and let Λ be the limit set of ?, i.e., the set of all infinite self-avoiding paths (called ends) through ? that begin at a vertex of the first generation. The limit set Λ is endowed with the metric d(ζ, ξ) = 2
−n
where n = n(ζ, ξ) is the index of the first generation where ζ and ξ differ. To each end ζ is associated the infinite sequence Φ(ζ) of
types of the vertices of ζ. Let Ω be the space of all such sequences. For any ergodic, shift-invariant probability measure
μ on Ω, define Ωμ to be the set of all μ-generic sequences, i.e., the set of all sequences ω such that each finite sequence v occurs in ω with limiting frequency μ(Ω(v)), where Ω(v) is the set of all ω′?Ω that begin with the word v. Then the Hausdorff dimension of Λ∩Φ−1 (Ωμ) in the metric d is
almost surely on the event of nonextinction, where h(μ) is the entropy of the measure μ and q(i, j) is the mean number of type-j offspring of a type-i individual. This extends a theorem of HAWKES [5], which shows that the Hausdorff dimension of the entire boundary at infinity is log2 α, where α is the Malthusian parameter.
Received: 30 June 1998 / Revised: 4 February 1999 相似文献
11.
Summary. Graeffe iteration was the choice algorithm for solving univariate polynomials in the XIX-th and early XX-th century. In this paper, a new variation of Graeffe iteration is given, suitable to IEEE floating-point arithmetics of modern digital computers. We prove that under a certain generic assumption the proposed algorithm converges. We also estimate the error after N iterations and the running cost. The main ideas from which this algorithm is built are: classical Graeffe iteration and Newton Diagrams, changes of scale (renormalization), and replacement of a difference technique by a differentiation one. The algorithm was implemented successfully and a number of numerical experiments are displayed. Received May 29, 1998 / Revised version received September 13, 1999 / Published online April 5, 2001 相似文献
12.
Let U
λ be the union of two unit intervals with gap λ. We show that U
λ is a self-similar set satisfying the open set condition if and only if U
λ can tile an interval by finitely many of its affine copies (admitting different dilations). Furthermore, each such λ can
be characterized as the spectrum of an irreducible double word which represents a tiling pattern. Some further considerations
of the set of all such λ’s, as well as the corresponding tiling patterns, are given.
The first author was partially supported by the RGC grant and the direct grant in CUHK, Fok Ying Tong Education Foundation
and NSFC (10571100). The second author was partially supported by NSFC (70371074) and NFSC (10571104). 相似文献
13.
Michel Talagrand 《Probability Theory and Related Fields》1998,112(4):545-563
Consider 0<α<1 and the Gaussian process Y(t) on ℝ
N
with covariance E(Y(s)Y(t))=|t|2α+|s|2α−|t−s|2α, where |t| is the Euclidean norm of t. Consider independent copies X
1,…,X
d
of Y and␣the process X(t)=(X
1(t),…,X
d
(t)) valued in ℝ
d
. When kN≤␣(k−1)αd, we show that the trajectories of X do not have k-multiple points. If N<αd and kN>(k−1)αd, the set of k-multiple points of the trajectories X is a countable union of sets of finite Hausdorff measure associated with the function ϕ(ɛ)=ɛ
k
N
/α−(
k
−1)
d
(loglog(1/ɛ))
k
. If N=αd, we show that the set of k-multiple points of the trajectories of X is a countable union of sets of finite Hausdorff measure associated with the function ϕ(ɛ)=ɛ
d
(log(1/ɛ) logloglog 1/ɛ)
k
. (This includes the case k=1.)
Received: 20 May 1997 / Revised version: 15 May 1998 相似文献
14.
Marc Arnaudon 《Probability Theory and Related Fields》1997,108(2):219-257
Summary. We prove that the derivative of a differentiable family X
t
(a) of continuous martingales in a manifold M is a martingale in the tangent space for the complete lift of the connection in M, provided that the derivative is bicontinuous in t and a. We consider a filtered probability space (Ω,(ℱ
t
)0≤
t
≤1, ℙ) such that all the real martingales have a continuous version, and a manifold M endowed with an analytic connection and such that the complexification of M has strong convex geometry. We prove that, given an analytic family a↦L(a) of random variable with values in M and such that L(0)≡x
0∈M, there exists an analytic family a↦X(a) of continuous martingales such that X
1(a)=L(a). For this, we investigate the convexity of the tangent spaces T
(
n
)
M, and we prove that any continuous martingale in any manifold can be uniformly approximated by a discrete martingale up to
a stopping time T such that ℙ(T<1) is arbitrarily small. We use this construction of families of martingales in complex analytic manifolds to prove that
every ℱ1-measurable random variable with values in a compact convex set V with convex geometry in a manifold with a C
1 connection is reachable by a V-valued martingale.
Received: 14 March 1996/In revised form: 12 November 1996 相似文献
15.
John Verzani 《Probability Theory and Related Fields》1997,107(4):517-526
Summary. For the Brownian path-valued process of Le Gall (or Brownian snake) in , the times at which the process is a cone path are considered as a function of the size of the cone and the terminal position
of the path. The results show that the paths for the path-valued process have local properties unlike those of a standard
Brownian motion.
Received: 29 January 1996 / In revised form: 21 June 1996 相似文献
16.
Becker-Kern Peter Meerschaert Mark M. Scheffler Hans-Peter 《Monatshefte für Mathematik》2003,140(2):91-101
The Hausdorff dimension of the sample paths of a stochastic process with stationary independent operator stable increments is computed. With probability one, every sample path has the same dimension, depending on the real parts of the eigenvalues of the operator stable exponent.Received May 28, 2002; in revised form October 2, 2002
Published online May 15, 2003 相似文献
17.
Julien Barral 《Probability Theory and Related Fields》1999,113(4):535-569
Here, a Mandelbrot measure is a statistically self-similar measure μ on the boundary of a c-ary tree, obtained by multiplying random weights indexed by the nodes of the tree. We take a particular interest in the random variable Y = ‖μ‖: we study the existence of finite moments of negative orders for Y, conditionally to Y > 0, and the continuity properties of Y with respect to the weights. Our results on moments make possible to study, with probability one, the existence of a local Hölder exponent for μ, almost everywhere with respect to another Mandelbrot measure, as well as to perform the multifractal analysis of μ, under hypotheses that are weaker than those usually assumed. 相似文献
18.
Rectifiable sets in metric and Banach spaces 总被引:9,自引:0,他引:9
19.
Herbert Zeitler 《Mathematische Semesterberichte》2002,49(2):185-208
Zusammenfassung. Die Arbeit behandelt Modelle des Bronchialbaumes. Es wird zun?chst die Ver?nderung der Querschnitte von Luftwegen bei Verzweigungen
untersucht. Dann geht es um „Strichb?ume”– Baumh?he, Zweigl?nge, überlappungsfreiheit, Selbst?hnlichkeit und Dimension. Schlie{?}lich
findet sich auch noch eine Diskussion zu einem wohlbekannten Dreiecksfraktal – Grenzkurve, Selbst?hnlichkeit, Dimension, Zusammenhang
mit den „Strichb?umen”. Anatomen haben zu dem Thema noch viele Anregungen und Fragen.
相似文献
20.
We show that in dimensions two or more a sequence of long range contact processes suitably rescaled in space and time converges to a super-Brownian motion with drift. As a consequence of this result we can improve the results of Bramson, Durrett, and Swindle (1989) by replacing their order of magnitude estimates of how close the critical value is to 1 with sharp asymptotics. Received: 2 February 1998 / Revised version: 28 August 1998 相似文献