Johannes Kugler

most citedLocal limit theorem for the maximum of a random walk

1 citations · 1 across the 3 of their papers we have counts for

collaborators

3 papers

math.PR2014★ 1 cited

Local limit theorem for the maximum of a random walk

Johannes Kugler

Consider a family of $Δ$ -latticed aperiodic random walks ${S^{(a)}, 0 \leq a \leq a_{0}}$ with increments $X_{i}^{(a)}$ and non-positive drift $- a$ . Suppose that $\sup_{a\le a_0}\mathbf{E…

math.PR2014

Heavy traffic and heavy tails for the maximum of a random walk

Denis Denisov, Johannes Kugler

Consider a family of random walks $S_{n}^{(a)} = X_{1}^{(a)} + \dots + X_{n}^{(a)}$ with negative drift $E X_{1}^{(a)} = - a < 0$ and finite variance $\mbox{var}(X_1^{(a)})=σ^2<\infty$.Let $…

math.PR2011

Upper bounds for the maximum of a random walk with negative drift

Johannes Kugler, Vitali Wachtel

Consider a random walk $S_{n} = \sum_{i = 0}^{n} X_{i}$ with negative drift. This paper deals with upper bounds for the maximum $M = max_{n \geq 1} S_{n}$ of this random walk in different settings…