arXiv subjects

Dimiter Tsvetkov

Publications and source records attributed to Dimiter Tsvetkov.

2 recordsLinked to original sources

arXiv2020

Positive periodic solutions for periodic predator-prey systems of Leslie-Gower or Holling-Tanner type

In this paper, we consider periodic predator-prey systems of Leslie-Gower or Holling-Tanner type, assuming that the coefficients are continuous positive $ω$-periodic functions. We prove an existence of positive $ω$-periodic solutions by means of operator method in Banach spaces with cones. No constructive conditions are required for the coefficients, besides the positivity and periodicity. At the end we point out that the used approach can be applied with minor changes for proving the existence of positive $ω$-periodic solutions even in the case of certain delays.

math.CA↗

arXiv2020

On the convergence of the Metropolis-Hastings Markov chains

In this paper we study Markov chains associated with the Metropolis-Hastings algorithm. We consider conditions under which the sequence of the successive densities of such a chain converges to the target density according to the total variation distance for any choice of the initial density. In particular we prove that the positiveness of the proposal density is enough for the chain to converge. The content of this work basically presents a stand alone proof that the reversibility along with the kernel positivity imply the convergence.

math.ST↗