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pro vyhledávání: '"Kutsenko, Anton A."'
Autor:
Kutsenko, Anton A.
For branching processes, the generating functions for limit distributions of so-called ratios of probabilities of rare events satisfy the Schr\"oder-type integral-functional equations. Excepting limited special cases, the corresponding equations can
Externí odkaz:
http://arxiv.org/abs/2403.02252
Autor:
Kutsenko, Anton A.
The classical Galton--Watson process works with a fixed probability of fission at each time step. One of the generalizations is that the probabilities depend on time. We consider one of the most complex and interesting cases when we do not know the e
Externí odkaz:
http://arxiv.org/abs/2309.13765
Autor:
Kutsenko, Anton A.
For the density of Galton-Watson processes in the Schr\"oder case, we derive a complete left tail asymptotic series consisting of power terms multiplied by periodic factors.
Comment: v.3 - minor update: Theorem is added
Comment: v.3 - minor update: Theorem is added
Externí odkaz:
http://arxiv.org/abs/2305.15088
Autor:
Kutsenko, Anton A.
It is known that the left tail asymptotic for supercritical branching processes in the Schr\"oder case satisfies a power law multiplied by some multiplicatively periodic function. We provide an explicit expression for this periodic function.
Externí odkaz:
http://arxiv.org/abs/2305.02812
Autor:
Kutsenko, Anton A
For the solutions $\Phi(z)$ of functional equations $\Phi(z)=P(z)+\Phi(Q(z))$, we derive a complete asymptotic of power series coefficients. As an application, we improve significantly an asymptotic of the number of $2,3$-trees with $n$ leaves given
Externí odkaz:
http://arxiv.org/abs/2302.12646
Autor:
Kutsenko, Anton A
We discuss approximations of the relative limit densities of descendants in Galton--Watson processes that follow from the Karlin--McGregor near-constancy phenomena. These approximations are based on the fast exponentially decaying Fourier coefficient
Externí odkaz:
http://arxiv.org/abs/2206.13647
Autor:
Kutsenko, Anton A.
We consider Bernoulli measures $\mu_p$ on the interval $[0,1]$. For the standard Lebesgue measure the digits $0$ and $1$ in the binary representation of real numbers appear with an equal probability $1/2$. For the Bernoulli measures, the digits $0$ a
Externí odkaz:
http://arxiv.org/abs/2204.04663
Autor:
Kutsenko, Anton A
Exponential stochastic compression is the process when every second cell of an infinite chain may increase its weight merging randomly with left, right, or both neighboring cells. The total mass conservation is assumed. After that, merged cells fill
Externí odkaz:
http://arxiv.org/abs/2202.04032
Autor:
Kutsenko, Anton A
We consider a specific dynamical system of groups formation. It is based simultaneously on a gradient competition between groups and a strong accumulation inside groups. Such a dynamical system demonstrates interesting behavior of densities of emergi
Externí odkaz:
http://arxiv.org/abs/2112.12733
Autor:
Kutsenko, Anton A.
A closed-form expression for the amplitudes of source waves in 2D discrete lattice with local and linear (waveguides) defects is derived. The numerical implementation of this analytic expression is demonstrated by several examples.
Externí odkaz:
http://arxiv.org/abs/2201.03427