24 citations · 48 across the 17 of their papers we have counts for
26 papers
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…
Stationary entrance chains and applications to random walks
Aleksandar Mijatovic, Vladislav Vysotsky
For a Markov chain with values in a Polish space, consider the entrance chain, obtained by sampling at the moments when it enters a fixed set from its complement .…
The isoperimetric problem for convex hulls and the large deviations rate functionals of random walks
Vladislav Vysotsky
We study the asymptotic behaviour of the most likely trajectories of a planar random walk that result in large deviations of the area of their convex hull. If the Laplace transform…
Persistence of AR() sequences with Rademacher innovations and linear mod transforms
Vladislav Vysotsky, Vitali Wachtel
We study the probability that an AR(1) Markov chain , where is a constant, stays non-negative for a long time. We find the exact asymptotics of th…
When is the rate function of a random vector strictly convex?
Vladislav Vysotsky
We give a necessary and sufficient condition for strict convexity of the rate function of a random vector in . This condition is always satisfied when the random vector has fi…
On the completion of Skorokhod space
Mikhail Lifshits, Vladislav Vysotsky
We consider the classical Skorokhod space and the space of continuous functions equipped with the standard Skorokhod distance . It is well known that neither $…