6 citations · 22 across the 19 of their papers we have counts for
16 papers · 1 filter
The maximal displacement of radially symmetric branching random walk in
Viktor Bezborodov, Nina Gantert
We consider discrete-time branching random walks with a radially symmetric distribution. Independently of each other individuals generate offspring whose relative locations are giv…
Interacting particle systems with continuous spins
Viktor Bezborodov, Luca Di Persio, Martin Friesen +1
We study a general class of interacting particle systems over a countable state space where on each site the particle mass follows a stochastic differen…
Explosion and non-explosion for the continuous-time frog model
Viktor Bezborodov, Luca Di Persio, Peter Kuchling
We consider the continuous-time frog model on . At time , there are particles at , each of which is represented by a random variable. In…
Non-triviality in a totally asymmetric one-dimensional Boolean percolation model on a half-line
Viktor Bezborodov
It is well known that there are two regimes in a standard one-dimensional Boolean percolation model: either the entire space is covered a.s., or the covered volume fraction is stri…
Linear and superlinear spread for continuous-time frog model
Viktor Bezborodov, Tyll Krueger
Consider a stochastic growth model on . Start with some active particle at the origin and sleeping particles elsewhere. The initial number of particles at $x \in \ma…
The continuous-time frog model can spread arbitrarily fast
Viktor Bezborodov, Luca Di Persio, Tyll Krueger
The aim of this work is to demonstrate that the continuous-time frog model can spread arbitrary fast. The set of sites visited by an active particle can become infinite in a finite…
Shape theorem for a one-dimensional growing particle system with a bounded number of occupants per site
Viktor Bezborodov, Luca Di Persio, Tyll Krueger
We consider a one-dimensional discrete-space birth process with a bounded number of particle per site. Under the assumptions of the finite range of interaction, translation invaria…
Fecundity regulation in a spatial birth-and-death process
Viktor Bezborodov, Luca Di Persio, Dmitri Finkelshtein +2
We study a Markov birth-and-death process on a space of locally finite configurations, which describes an ecological model with a density dependent fecundity regulation mechanism.…
Spatial growth processes with long range dispersion: microscopics, mesoscopics, and discrepancy in spread rate
Viktor Bezborodov, Luca Di Persio, Tyll Krueger +1
We consider the speed of propagation of a {continuous-time continuous-space} branching random walk with the additional restriction that the birth rate at any spatial point cannot e…
Maximal irreducibility measure for spatial birth-and-death processes
Viktor Bezborodov, Luca Di Persio
We prove that under certain general conditions on the birth and death rates the Lebesgue-Poisson measure is a maximal irreducibility measure for the spatial birth-and-death process…
Asymptotic shape and the speed of propagation of continuous-time continuous-space birth processes
Viktor Bezborodov, Luca Di Persio, Tyll Krueger +2
We formulate and prove a shape theorem for a continuous-time continuous-space stochastic growth model under certain general conditions. Similarly to the classical lattice growth mo…
Option pricing with fractional stochastic volatility and discontinuous payoff function of polynomial growth
Viktor Bezborodov, Luca Di Persio, Yuliya Mishura
We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework cha…
An exponential estimate for the extinction time of the branching random walk on a cube
Viktor Bezborodov
We prove the exponential estimate \begin{equation*} P \{ s < τ< \infty \} \leq C e^{-q s}, \quad s \geq 0, \end{equation*} where are constants and is the extinction…
Spatial birth-and-death processes with a finite number of particles
Viktor Bezborodov, Luca Di Persio
Spatial birth-and-death processes with time dependent rates are obtained as solutions to certain stochastic equations. The existence, uniqueness, uniqueness in law and the strong M…
Lattice birth-and-death processes
Viktor Bezborodov, Yuri Kondratiev, Oleksandr Kutoviy
Lattice birth-and-death Markov dynamics of particle systems with spins from the set of non-negative integers are constructed as unique solutions to certain stochastic equations. Pa…
Markov birth-and-death dynamics of populations
Viktor Bezborodov
Spatial birth-and-death processes with a finite number of particles are obtained as unique solutions to certain stochastic equations. Conditions are given for existence and uniquen…