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  • Author or Editor: Antonia Földes x
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Summary Some topics of our twenty some years of joint work is discussed. Just to name a few; joint behavior of the maximum of the Wiener process and its location, global and local almost sure limit theorems,  strong approximation of the planar local time difference, a general Strassen type theorem, maximal local time on subsets.

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Abstract  

This is a brief account on how we have entertained ourselves in the last two years, that is, a summary of the results we have obtained in a joint work with E. Csáki, M. Csörgő and P. Révész on random walks on a comb.

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We study the path behavior of the symmetric walk on some special comb-type subsets of ℤ2 which are obtained from ℤ2 by generalizing the comb having finitely many horizontal lines instead of one.

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Considering a simple symmetric random walk in dimension d ≧ 3, we study the almost sure joint asymptotic behavior of two objects: first the local times of a pair of neighboring points, then the local time of a point and the occupation time of the surface of the unit ball around it.

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