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Random paths with bounded local time

Itai Benjamini, Nathanaël Berestycki (2010)

Journal of the European Mathematical Society

We consider one-dimensional Brownian motion conditioned (in a suitable sense) to have a local time at every point and at every moment bounded by some fixed constant. Our main result shows that a phenomenon of entropic repulsion occurs: that is, this process is ballistic and has an asymptotic velocity approximately 4.58... as high as required by the conditioning (the exact value of this constant involves the first zero of a Bessel function). We also study the random walk case and show that the process...

Superposition of diffusions with linear generator and its multifractal limit process

End Iglói, György Terdik (2003)

ESAIM: Probability and Statistics

In this paper a new multifractal stochastic process called Limit of the Integrated Superposition of Diffusion processes with Linear differencial Generator (LISDLG) is presented which realistically characterizes the network traffic multifractality. Several properties of the LISDLG model are presented including long range dependence, cumulants, logarithm of the characteristic function, dilative stability, spectrum and bispectrum. The model captures higher-order statistics by the cumulants. The relevance...

Superposition of Diffusions with Linear Generator and its Multifractal Limit Process

Endre Iglói, György Terdik (2010)

ESAIM: Probability and Statistics

In this paper a new multifractal stochastic process called Limit of the Integrated Superposition of Diffusion processes with Linear differencial Generator (LISDLG) is presented which realistically characterizes the network traffic multifractality. Several properties of the LISDLG model are presented including long range dependence, cumulants, logarithm of the characteristic function, dilative stability, spectrum and bispectrum. The model captures higher-order statistics by the cumulants. The relevance...

The renormalization transformation for two-type branching models

D. A. Dawson, A. Greven, F. den Hollander, Rongfeng Sun, J. M. Swart (2008)

Annales de l'I.H.P. Probabilités et statistiques

This paper studies countable systems of linearly and hierarchically interacting diffusions taking values in the positive quadrant. These systems arise in population dynamics for two types of individuals migrating between and interacting within colonies. Their large-scale space–time behavior can be studied by means of a renormalization program. This program, which has been carried out successfully in a number of other cases (mostly one-dimensional), is based on the construction and the analysis of...

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