V. Wachtel

activity

20132026

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5 papers · 1 filter

math.PR2026

Broadcasting on Random Trees: Martingale Methods and Error Bounds

Tayfun Kardas, Vsevolod Shneer, Vitali Wachtel

The broadcasting problem on trees concerns the transmission of binary information along the edges of a tree. In the formulation studied here, each vertex carries one of two colours…

math.PR2023

Persistence of AR( $1$ ) sequences with Rademacher innovations and linear mod $1$ transforms

Vladislav Vysotsky, Vitali Wachtel

We study the probability that an AR(1) Markov chain $X_{n + 1} = a X_{n} + ξ_{n + 1}$ , where $a \in (0, 1)$ is a constant, stays non-negative for a long time. We find the exact asymptotics of th…

math.PR2022

Green function for an asymptotically stable random walk in a half space

Denis Denisov, Vitali Wachtel

We consider an asymptotically stable multidimensional random walk $S (n) = (S_{1} (n), \dots, S_{d} (n))$ . Let $τ_{x} := min {n > 0 : x_{1} + S_{1} (n) \leq 0}$ be the first time the random walk $S(n)…

math.PR2022

Persistence of autoregressive sequences with logarithmic tails

Denis Denisov, Gunter Hinrich, Martin Kolb +1

We consider autoregressive sequences $X_{n} = a X_{n - 1} + ξ_{n}$ and $M_{n} = max {a M_{n - 1}, ξ_{n}}$ with a constant $a \in (0, 1)$ and with positive, independent and identically distributed innova…

math.PR2013

Tail asymptotics for the supercritical Galton-Watson process in the heavy-tailed case

Denis Denisov, Dmitry Korshunov, Vitali Wachtel

As well known, for a supercritical Galton-Watson process $Z_{n}$ whose offspring distribution has mean $m > 1$ , the ratio $W_{n} := Z_{n} / m^{n}$ has a.s. limit, say $W$ . We study tail behaviou…

Broadcasting on Random Trees: Martingale Methods and Error Bounds

Persistence of AR(1) sequences with Rademacher innovations and linear mod 1 transforms

Green function for an asymptotically stable random walk in a half space

Persistence of autoregressive sequences with logarithmic tails

Tail asymptotics for the supercritical Galton-Watson process in the heavy-tailed case

Persistence of AR( $1$ ) sequences with Rademacher innovations and linear mod $1$ transforms