V. Vysotsky

collaborators

3 papers

math.PR2026

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 $X_{n + 1} = a X_{n} + I^¾_{n + 1}$ , where $a \in (0, 1)$ is a constant, stays non-negative for a long time. We find the exact asymptotics of t…

math.PR2025

Stationary switching random walks

Vladislav Vysotsky

A switching random walk, commonly known under the misnomer `oscillating random walk', is a real-valued Markov chain whose distribution of increments is determined by the sign of th…

math.PR2025

Stationary entrance chains and applications to random walks

Aleksandar Mijatovic, Vladislav Vysotsky

For a Markov chain $Y$ with values in a Polish space, consider the entrance chain, obtained by sampling $Y$ at the moments when it enters a fixed set $A$ from its complement $A^{c}$ .…

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

Stationary switching random walks

Stationary entrance chains and applications to random walks

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