Asymptotic Behavior of Eigenvalues of Certain Integral Operators
We study different types of asymptotic behaviour in the set of (infinite dimensional) nonhomogeneous chains of stochastic operators acting on L¹(μ) spaces. In order to examine its structure we consider different norm and strong operator topologies. To describe the nature of the set of nonhomogeneous chains of Markov operators with a particular limit behaviour we use the category theorem of Baire. We show that the geometric structure of the set of those stochastic operators which have asymptotically...
Asymptotic convergence theorems for semigroups of nonnegative operators on a Banach lattice, on C(X) and on (1 ≤ p ≤ ∞) are proved. The general results are applied to a class of semigroups generated by some differential equations.
The problem to be treated in this note is concerned with the asymptotic behaviour of stochastic semigroups, as the time becomes very large. The subject is largely motived by the Theory of Markov processes. Stochastic semigroups usually arise from pure probabilistic problems such as random walks stochastic differential equations and many others.An outline of the paper is as follows. Section one deals with the basic definitions relative to K-positivity and stochastic semigroups. Asymptotic behaviour...
Asymptotic convergence theorems for nonnegative operators on Banach lattices, on , on C(X) and on are proved. The general results are applied to a class of integral operators on L¹.
A new criterion of asymptotic periodicity of Markov operators on , established in [3], is extended to the class of Markov operators on signed measures.
New sufficient conditions for asymptotic stability of Markov operators are given. These criteria are applied to a class of Volterra type integral operators with advanced argument.