4 citations · 6 across the 8 of their papers we have counts for
8 papers · 1 filter
Subcritical branching processes in random environment with immigration stopped at zero
Doudou Li, Vladimir Vatutin, Mei Zhang
We consider subcritical branching processes with immigration which evolve under the influence of a random environment and study the tail distribution of life periods of such proces…
Subcritical multitype branching process in random environment
Vladimir Vatutin, Vitali Wachtel
We study the asymptotic behaviour of the survival probability of a multitype branching process in random environment. The class of processes we consider here corresponds, in the on…
A two-type Bellman--Harris process initiated by a large number of particles
Vladimir Vatutin, Alexander Iksanov, Valentin Topchii
We investigate a two-type critical Bellman--Harris branching process with the following properties: the tail of the life-length distribution of the first type particles is of order…
Weak convergence of finite-dimensional distributions of the number of empty boxes in the Bernoulli sieve
Alexander Iksanov, Alexander Marynych, Vladimir Vatutin
The Bernoulli sieve is a random allocation scheme obtained by placing independent points with the uniform [0,1] law into the intervals made up by successive positions of a multipli…
Subcritical branching processes in random environment without Cramer condition
Vladimir Vatutin, Xinghua Zheng
A subcritical branching process in random environment (BPRE) is considered whose associated random walk does not satisfy the Cramer condition. The asymptotics for the survival prob…
Multitype branching processes with immigration in random environment and polling systems
Vladimir Vatutin
For multitype branching processes with immigration evolving in a random environment and producing a final product we find the tail distribution of the size of the final product acc…
Local probabilities for random walks conditioned to stay positive
Vladimir Vatutin, Vitali Wachtel
Let S_0=0,{S_n, n>0} be a random walk generated by a sequence of i.i.d. random variables X_1,X_2,... and let τ^{-} be the first descending ladder epoch. Assuming that the distribut…
Local limit theorems for ladder epochs
Vladimir Vatutin, Vitali Wachtel
Let {S_n, n=0,1,2,...} be a random walk generated by a sequence of i.i.d. random variables X_1, X_2,... and let tau be the first descending ladder epoch. Assuming that the distribu…