Asymptotics for Random Walks
with Dependent Heavy-Tailed Increments

Korshunov, Dmitry (Novosibirsk, Russia)
korshunov@math.nsc.ru

(joint work with Sabine Schlegel and Volker Schmidt)

In our talk, we consider a random walk $\{S_n\}$with dependent heavy-tailed increments and negative drift. We study the asymptotics for the tail probability ${\bf P}\{\sup_n S_n\gt x\}$as $x\to\infty$.If the increments of $\{S_n\}$ are independent, then the exact asymptotic behaviour of ${\bf P}\{\sup_n S_n\gt x\}$ is well-known in so-called sub-exponential case. In our talk, we discuss the case that the increments are given as a one-sided asymptotically stationary linear process. It turns out that the tail behaviour of $\sup_n S_n$ heavily depends on the coefficients of this linear process.