Department of Stochastics (Budapest University of Technology and Economics)
Participants
Hernáth, Szabolcs Szabados, Tamás Székely, Balázs Tóth, Rozália Hajnal
Starting date
2003-01-01
Closing date
2007-12-31
Funding (in million HUF)
4.633
FTE (full time equivalent)
0.00
state
closed project
Final report
Results in Hungarian
Az OTKA pályázatunk keretében folytatott kutatásaink eddig 13 cikkben jelentek meg. További eredményeink publikálása folyamatban van. Legfontosabb eredményeink a következő cím szavakban írhatók le:
1. Determinisztikus iterált függvényrendszerek (IFS) véletlen perturbációi.
2. Véletlen Cantor halmazok algebrai különbsége.
3. Sztochasztikus integrálás véletlen sétával.
4. Átlagosan összehúzó IFS-ek.
5. Hausdorff dimenzió hiperbolikus attraktorokra.
6. Véletlen összegek eloszlásának abszolút folytonossága.
7. Különböző valószínűséggel megkonstruált Bernoulli konvolúciók abszolút folytonossága.
8. Internet forgalom modellezése multifractal analízissel.
Results in English
The results we have accomplisehed during our project have been published in 13 research papers. The publication of some of our further results are in process. Our most important achievments are related to the following fields:
1. Random perturbation of deterministic IFS (iterated function systems).
2. Algebraic difference of random Cantor sets.
3. Stochastic integrals Stochastic Integration Based on Simple, Symmetric RandomWalks.
4. IFS that are contracting on average.
5. Hausdorff dimension for hyperbolic attractors.
6. Absolute continuity of the distribution of random sums.
7. Absolute continuity of Bernoulli convolutions with different probabilities.
8. A random multifractal model with a given spectrum for modelling internet trafic.
Simon Károly, Tóth Rozália Hajnal: Absloute Continuity of the Distribution of Random Sums with Digits 0, 1, ... m-1, Real Analysis Exchange 30 (2004/05), no. 1, 397--409, 2005
T. Szabados and B. Székely: An elementary approach to Brownian local time, Periodica Mathematica Hungarica, 51, 77-98, 2005
Ai Hua Fan, Simon Károly, Tóth Hajnal: Contracting on Average Random IFS with Repelling Fixed Point, Journal of Stat. Phys. 122 (2006), no. 1, 169--193., 2006
Y. Peres, K. Simon, B. Solomyak: Absolute continuity for random iterated function systems with overlaps., J. London Math. Soc. (2) 74 (2006) 739-756, 2006
T. Jordan, M. Pollicott, K. Simon: Hausdorff dimension for randomly perturbed self affine attractors., Communications in Math. Phys. 270 (2007), 519-544, 2007
A. Manning, K.Simon: Subadditive pressure for triangular maps., Nonlinearity Volume 20, Number 1, January (2007), 133-149., 2007
F. Hofbauer, P. Raith, K. Simon,: Hausdorff dimension for some hyperbolic attractors with overlaps and without finite Markov partition, Ergodic Theory Dynam. Systems 27 (4) (2007), 1143-1165., 2007
T. Jordan, K. Simon: Multifractal analysis for Birkhoff averages for some self-affine IFS., Dynamical Systems An International Journal, Volume 22 Issue 4, 469 (2007) 469-483, 2007
K Simon, B. Solomyak,: Visibility for self-similar sets of dimension one in the plane., Real Anal. Exchange 32 (2006/07), no. 1, 67--78, 2007
M. Dekking, K. Simon: On the size of the algebraic difference of two random Cantor sets., Random Structures and Algorithms 32 (2008) 205-222, 2008
Hajnal R. Tóth: Infinite Bernoulli convolutions with different probabilities, Discrete and continuous dynamical systems vol. 21 Number 2 595-600, 2008
T. Szabados, B. Székely: Stochastic Integration Based on Simple, Symmetric Random Walks, Journal of Theoretical Probability, online http://www.springerlink.com/content/jh6372k1045513nt/fulltext.pdf, 2008
B. Székely, T.D. Dang, I. Maricza, S. Molnár: A Random Multifractal Model with a Given Spectrum, Stoch. Models 22 , no. 3, 483--508, 2006
