N. Patzschke and U. Z ahle, Self-similar random measures IV. The recursive construction model of Falconer, Graf, Mauldin and Williams, Math. Nachr., 149(1990), 285-302.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....by the rotational parts of (S 1 ; Sn ) is normalized Haar measure on G and a(x) b(x) are constants depending on x and B. 10 P. M orters and D. Preiss The measure distribution P in Graf s result has been described before as the natural randomization of by Patzschke and U. Z ahle [PaZU]. Other explicit formulae for tangent measure distributions in self similar situations may be found in [APa] for the case of random self similar sets, in [KM] for the case of hyperbolic Cantor sets and in [M o3] for the paths of Brownian motion. The main result While it is easy to prove the ....

....origin as a typical point . More precisely, a measure distribution P on M(R d ) is an self similar random measure if P is a Palm measure invariant under the rescaling group (S ) 0 . This concept has been subject of investigations by Patzschke, U. Z ahle and M. Z ahle, see for example [PaZU] and [PaZM] In particular, they have studied the relation of the concept to statistically self similar measures in the constructive sense. We extend the notion of self similar random measures to allow, in the natural way, for the possibility that P (f g) 0 and or that the total mass of P may ....

N. Patzschke and U. Zahle. Self similar random measures IV. The recursive construction model of Falconer, Graf, Mauldin and Williams. Math. Nachr., 149:285-302, 1990.

....point of the random measure. We can interpret Palm distributions as those distributions which have the origin as a typical point of their realizations (see [22] for details) This concept of statistical self similarity has been studied by Patzschke, U. Z ahle and M. Z ahle for example in [18], 20] where also its relation to statistically self similar measures in the constructive sense was investigated. We get the following theorem (recall that we did not require to be self similar in any sense) Theorem 2.8 At almost all points x every tangent measure distribution P 2 P( x) de ....

N. Patzschke and U. Z ahle, Self-similar random measures IV. The recursive construction model of Falconer, Graf, Mauldin and Williams, Math. Nachr., 149(1990), 285-302.

....origin as a typical point . More precisely, a measure distribution P on M(R d ) is an ff self similar random measure if P is a Palm measure invariant under the rescaling group (S ff ) 0 . This concept has been subject of investigations by Patzschke, U. Zahle and M. Zahle, see for example [PaZU] and [PaZM] In particular, they have studied the relation of the concept to statistically self similar measures in the constructive sense. Using the notion of ff self similar random measures, we may reformulate Theorem 1 as Theorem 3. Let ff 0 and 2 M(R d ) be any measure. Then, at ....

N. Patzschke and U. Zahle. Self-similar random measures IV. The recursive construction model of Falconer, Graf, Mauldin and Williams. Math. Nachr., 149:285--302, 1990.

....of ergodic theory, local characteristics of self similar sets. This idea is due to Bedford and Fisher (see [4] Closely related ideas can be found in the work of U. Zahle on self similar random measures (see [19] which is continued in a series of joint work with Patzschke and M. Zahle (see e.g. [18], 17] Bandt joined these ideas and defined the tangent measure distributions of a measure at a point as limiting distributions of sequences of natural probability distributions on (rescaled) enlargements of the measure about this point. Roughly speaking, the weight that a tangent measure ....

N. Patzschke and U. Z ahle. Self-similar random measures IV. The recursive construction model of Falconer, Graf, Mauldin and Williams. Math. Nachr., 149:285--302, 1990.

....we give an application to multifractal analysis of the random self similar fractal. 1. Notations In this section we recall the defintion of self similar sets and self similar measures, and give some properties. A more detailed introduction and the proofs of the properties may be found in [PZ] and in [AP] Let K ae R d be a fixed compact set with K = int K. We are given a positive integer N 2 and a probability measure on Sim N Theta [0; 1] N , where Sim is the space of all similarities of R d equipped with the usual topology of uniform convergence on compact sets. In this ....

....and write T ( ffi Delta . Then S j (T ) S j ( and p j (T ) p j ( We will denote the objects generated by T with a superscript , e.g. S j ( S j (T ) Phi = Phi T , and so on. The measures Phi and Psi and the set Xi fulfill the following invariances (cf. [AP, PZ]) THE STRONG OPEN SET CONDITION IN THE RANDOM CASE 2121 Theorem 2. Let Gamma be a Markov stopping. Then (i) Psi = X 2 Gamma p Psi ffi Delta Gamma1 , where the Psi are i. i. d. copies of Psi and independent of F Gamma . ii) Phi = X 2 Gamma p Phi ffi S Gamma1 ....

N. Patzschke and U. Zahle, Self--similar random measures IV. --- The recursive construction model of Falconer, Graf, and Mauldin and Williams. Math. Nachr. 149 (1990), 285 -- 302. MR 92j:28007

....generalized dimensions are calculated. The last section deals with the tangential distribution of the random self similar measure Phi. 2. Random self similar measures In this section we recall the definition and some properties of random self similar measures. We use the same notions as in [PZU] and in [PZM] For further details see these papers. 8 Math. Nachr. 181 (1996) Let K ae IR d be a fixed compact set with K = int K. Without loss of generality we assume diamK = 1. Our primary object is a probability measure on Sim N Theta[0; 1] N , where Sim is the set of all ....

Patzschke, N., and Z ahle, U.: Self--Similar Random Measures IV. --- The Recursive Construction Model of Falconer, Graf, and Mauldin and Williams. Math. Nachr. 149 (1990), 285 -- 302

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N. Patzschke and U. Z ahle, Self-similar random measures IV. The recursive construction model of Falconer, Graf, Mauldin and Williams, Math. Nachr., 149(1990), 285-302.

No context found.

N. Patzschke and U. Z ahle. Self-similar random measures IV. The recursive construction model of Falconer, Graf, Mauldin and Williams. Math. Nachr., 149:285--302, 1990.

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Patzschke, N., and Z ahle, U., Self--similar random measures IV. --- The recursive construction model of Falconer, Graf, and Mauldin and Williams, Math. Nachr. 149 (1990), 285 -- 302

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