Seminarium:
Teoria prawdopodobieństwa i modelowanie stochastyczne
Osoba referująca:
Aleksander Iksanov, Valeria Kotelnikova (Taras Shevchenko National University of Kyiv)
Data:
czwartek, 14. Maj 2026 - 13:15
Sala:
603
Opis:
Speaker: Aleksander Iksanov
Title: On local large deviations for decoupled random walks
Abstract: A decoupled random walk is a sequence S1, S2,… of independent random variables such that, for each integer n, Sn has the same distribution as the position at time n of a standard random walk with nonnegative jumps. A decoupled renewal process is the counting process (N(t)) defined by the number of visits of (Sn) to the closed interval [0,t]. Under various assumptions on the distribution tail of S1 I shall present logarithmic asymptotics for the local large deviation probabilities P{N(t) =[b EN(t)]} as t approaches infinity for a fixed positive constant b. It will be explained how to derive a logarithmic local large deviations asymptotic for the counting process associated with determinantal point processes with the Mittag-Leffler kernel. The talk is based on a joint work with Dariusz Buraczewski and Alexander Marynych.
Speaker: Valeria Kotelnikova
Title: On tail behavior of infinite sums of independent indicators
Abstract: Let $Y=\sum_{k\ge 1} 1_{A_k}$ be an infinite sum of the indicators of independent events. I will speak on a precise (as opposed to logarithmic) first-order asymptotic behavior of the tail probabilities $\mathbb{P}\{Y \ge n\}$ and the point probabilities $\mathbb{P}\{Y = n\}$ as $n \to \infty$. The talk is based on the recent joint work with Alexander Iksanov.
Title: On local large deviations for decoupled random walks
Abstract: A decoupled random walk is a sequence S1, S2,… of independent random variables such that, for each integer n, Sn has the same distribution as the position at time n of a standard random walk with nonnegative jumps. A decoupled renewal process is the counting process (N(t)) defined by the number of visits of (Sn) to the closed interval [0,t]. Under various assumptions on the distribution tail of S1 I shall present logarithmic asymptotics for the local large deviation probabilities P{N(t) =[b EN(t)]} as t approaches infinity for a fixed positive constant b. It will be explained how to derive a logarithmic local large deviations asymptotic for the counting process associated with determinantal point processes with the Mittag-Leffler kernel. The talk is based on a joint work with Dariusz Buraczewski and Alexander Marynych.
Speaker: Valeria Kotelnikova
Title: On tail behavior of infinite sums of independent indicators
Abstract: Let $Y=\sum_{k\ge 1} 1_{A_k}$ be an infinite sum of the indicators of independent events. I will speak on a precise (as opposed to logarithmic) first-order asymptotic behavior of the tail probabilities $\mathbb{P}\{Y \ge n\}$ and the point probabilities $\mathbb{P}\{Y = n\}$ as $n \to \infty$. The talk is based on the recent joint work with Alexander Iksanov.