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Hausdorff dimension of invariant measures related to Poisson driven stochastic differential equations

Tomasz Bielaczyc — 2011

Annales Polonici Mathematici

It is shown that the Hausdorff dimension of an invariant measure generated by a Poisson driven stochastic differential equation is greater than or equal to 1.

Generic Properties of Continuous Iterated Function Systems with Place Dependent Probabilities

Tomasz Bielaczyc — 2007

Bulletin of the Polish Academy of Sciences. Mathematics

It is shown that for a typical continuous learning system defined on a compact convex subset of ℝⁿ the Hausdorff dimension of its invariant measure is equal to zero.

Generic properties of iterated function systems with place dependent probabilities.

Bielaczyc, Tomasz — 2006

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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