15 citations · 15 across the 11 of their papers we have counts for
11 papers · 1 filter
Population size of critical Galton-Watson processes under small deviations and infinite variance
Vladimir Vatutin, Elena Dyakonova
We study the evolution of the population size distribution of a critical Galton-Watson process with infinite variance of the offspring size of particles assuming that the populatio…
Limit theorems for critical branching processes in an extremely unfavorable random environment
Vladimir Vatutin, Elena Dyakonova
Let be a critical branching process in random environment and be its associated random walk. Assuming that the increments distribution of th…
Reduced critical branching processes in non-favorable random environment
V. A. Vatutin, E. E. Dyakonova
Let be a critical branching process in i.i.d. random environment, be the number of particles in the process at moment $0\leq r\leq n-…
Small deviations for critical Galton-Watson processes with infinite variance
Vladimir Vatutin, Elena Dyakonova, Yakubdjan Khusanbaev
We study the asymptotic behavior of small deviation probabilities for the critical Galton-Watson processes with infinite variance of the offspring sizes of particles and apply the…
On the prospective minimum of the random walk conditioned to stay non-negative
Vladimir Vatutin, Elena Dyakonova
Let \begin{equation*} S_{0}=0,\quad S_{n}=X_{1}+...+X_{n},\ n\geq 1, \end{equation*} be a random walk whose increments belong without centering to the domain of attraction of a sta…
Some functionals for random walks and critical branching processes in extreme random environment
Congzao Dong, Elena Dyakonova, Vladimir Vatutin
Let be a random walk whose increment distribution belongs without centering to the domain of attraction of an -stable law, i.e., there are som…
Survival probability for a class of multitype subcritical branching processes in random environment
Vladimir Vatutin, Elena Dyakonova
We study the asymptotic behaviour of the survival probability of a multi-type branching processes in random environment. The class of processes we consider corresponds, in the one-…
How many families survive for a long time
V. A. Vatutin, E. E. Dyakonova
A critical branching process in a random environment generated by a sequence of independent and identically distributed random reproduction laws…
Branching processes in random environment which extinct at a given moment
C. Boeinghoff, E. E. Dyakonova, G. Kersting +1
Let be a critical branching process in random environment and let be its moment of extinction. Under the annealed approach we prove, as a lim…
Coalescent approximation for structured populations in a stationary random environment
Serik Sagitov, Peter Jagers, Vladimir Vatutin
We establish convergence to the Kingman coalescent for the genealogy of a geographically - or otherwise - structured version of the Wright-Fisher population model with fast migrati…
On the asymptotic behaviour of random recursive trees in random environment
Konstantin Borovkov, Vladimir Vatutin
We consider growing random recursive trees in random environment, in which at each step a new vertex is attached (by an edge of a random length) to an existing tree vertex accordin…