Maximal local time of a d-dimensional simple random walk on subsets
Strong theorems are given for the maximal local time on balls and subspaces for the $d$-dimensional simple symmetric random walk.
math.PR↗
arXiv subjects
Endre Csáki
Publications and source records attributed to Endre Csáki.
On Vervaat and Vervaat-error type processes for partial sums and renewals
We study the asymptotic behaviour of stochastic processes that are generated by sums of partial sums of i.i.d. random variables and their renewals. We conclude that these processes cannot converge weakly to any nondegenerate random element of the space $D[0,1]$. On the other hand we show that their properly normalized integrals as Vervaat-type stochastic processes converge weakly to a squared Wiener process. Moreover, we also deal with the asymptotic behaviour of the deviations of these processes, the so-called Vervaat-error type processes.
math.PR↗
An embedding for the Kesten-Spitzer random walk in random scenery
For one-dimensional simple random walk in a general i.i.d. scenery and its limiting process we construct a coupling with explicit rate of approximation extending a recent result for Gaussian sceneries due to Khoshnevisan and Lewis. Furthermore we explicity identify the constant in the law of iterated logarithm.
math.PR↗