Zobrazeno 1 - 10
of 81
pro vyhledávání: '"Vysotsky, Vladislav"'
Autor:
Vysotsky, Vladislav
A switching random walk, commonly known under the misnomer `oscillating random walk', is a real-valued Markov chain such that the distribution of its increments depends only on the sign of the current position. In this note we find invariant measures
Externí odkaz:
http://arxiv.org/abs/2403.04620
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 $A^c$. Similarly, consider the exit chain, obtained by sampling $Y$ at the ex
Externí odkaz:
http://arxiv.org/abs/2403.00619
The isoperimetric problem for convex hulls and the large deviations rate functionals of random walks
Autor:
Vysotsky, Vladislav
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 of the increments is finite on $R^2$, such a scaled limit trajectory
Externí odkaz:
http://arxiv.org/abs/2306.12359
Autor:
Vysotsky, Vladislav, Wachtel, Vitali
We study the probability that an AR(1) Markov chain $X_{n+1}=aX_n+\xi_{n+1}$, where $a\in(0,1)$ is a constant, stays non-negative for a long time. We find the exact asymptotics of this probability and the weak limit of $X_n$ conditioned to stay non-n
Externí odkaz:
http://arxiv.org/abs/2305.10038
Autor:
Vysotsky, Vladislav
Publikováno v:
In Stochastic Processes and their Applications February 2025 180
Autor:
Vysotsky, Vladislav
We give a necessary and sufficient condition for strict convexity of the rate function of a random vector in $R^d$. This condition is always satisfied when the random vector has finite Laplace transform. We also completely describe the effective doma
Externí odkaz:
http://arxiv.org/abs/2009.06809
Autor:
Lifshits, Mikhail, Vysotsky, Vladislav
We consider the classical Skorokhod space $D[0,1]$ and the space of continuous functions $C[0,1]$ equipped with the standard Skorokhod distance $\rho$. It is well known that neither $(D[0,1],\rho)$ nor $(C[0,1],\rho)$ is complete. We provide an expli
Externí odkaz:
http://arxiv.org/abs/2003.10787
We prove distributional limit theorems for the length of the largest convex minorant of a one-dimensional random walk with independent identically distributed increments. Depending on the increment law, there are several regimes with different limit
Externí odkaz:
http://arxiv.org/abs/1909.12322
Contraction principle for trajectories of random walks and Cramer's theorem for kernel-weighted sums
Autor:
Vysotsky, Vladislav
In 2013 A.A. Borovkov and A.A. Mogulskii proved a weaker-than-standard "metric" large deviations principle (LDP) for trajectories of random walks in $R^d$ whose increments have the Laplace transform finite in a neighbourhood of zero. We prove that ge
Externí odkaz:
http://arxiv.org/abs/1909.00374
We prove that for a random walk on the real line whose increments have zero mean and are either integer-valued or spread out (i.e. the distributions of the steps of the walk are eventually non-singular), the Markov chain of overshoots above a fixed l
Externí odkaz:
http://arxiv.org/abs/1812.05909