V. Wachtel

activity

20132026

most citedHarmonic measure in a multidimensional gambler's problem

1 citations · 1 across the 6 of their papers we have counts for

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Showing 2022Show all

3 papers · 1 filter

math.PR2022★ 1 cited

Harmonic measure in a multidimensional gambler's problem

Denis Denisov, Vitali Wachtel

We consider a random walk in a truncated cone $K_{N}$ , which is obtained by slicing cone $K$ by a hyperplane at a growing level of order $N$ . We study the behaviour of the Green func…

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…