‎In the present paper we investigate the $L_1$-weak ergodicity of‎ ‎nonhomogeneous continuous-time Markov processes with general state‎ ‎spaces‎. ‎We provide a necessary and sufficient condition for such‎ ‎processes to satisfy the $L_1$-weak ergodicity‎. ‎Moreover‎, ‎we apply‎ ‎the obtained results to establish $L_1$-weak ergodicity of quadratic‎ ‎stochastic processes‎.

‎in the present paper we investigate the $l_1$-weak ergodicity of‎ ‎nonhomogeneous continuous-time markov processes with general state‎ ‎spaces‎. ‎we provide a necessary and sufficient condition for such‎ ‎processes to satisfy the $l_1$-weak ergodicity‎. ‎moreover‎, ‎we apply‎ ‎the obtained results to establish $l_1$-weak ergodicity of quadratic‎ ‎stochastic processes‎.

Under natural conditions, we prove exponential ergodicity in the \( L_1\)-Wasserstein distance of two-type continuous-state branching processes Lévy random environments with immigration. Furthermore, express precisely parameters exponent. The coupling method and conditioned property play an important role approach. Using tool superprocesses, total variation is also proved.

A Markov polling system with infinitely many stations is studied. The topic is the ergodicity of the infinite-dimensional process of queue lengths. For the infinite-dimensional process, the usual type of ergodicity cannot prevail in general and we introduce a modified concept of ergodicity, namely, weak ergodicity. It means the convergence of finitedimensional distributions of the process. We g...

The problem of finding \emph{distance} between \emph{pattern} of length $m$ and \emph{text} of length $n$ is a typical way of generalizing pattern matching to incorporate dissimilarity score. For both Hamming and $L_1$ distances only a super linear upper bound $\widetilde{O}(n\sqrt{m})$ are known, which prompts the question of relaxing the problem: either by asking for $1 \pm \varepsilon$ appro...