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.
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.
Authors:Endre Csáki, Antónia Földes and Pál Révész
Considering a simple symmetric random walk in dimension
≧ 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.