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Hongyan Sun

Publications and source records attributed to Hongyan Sun.

4 recordsLinked to original sources
arXiv2022

Regeneration of branching processes with immigration in varying environments

In this paper, we consider certain linear-fractional branching processes with immigration in varying environments. For $n\ge0,$ let $Z_n$ counts the number of individuals of the $n$-th generation, which excludes the immigrant which enters into the system at time $n.$ We call $n$ a regeneration time if $Z_n=0.$ We give first a criterion for the finiteness or infiniteness of the number of regeneration times. Then, we construct some concrete examples to exhibit the strange phenomena caused by the so-called varying environments. It may happen that the process is extinct but there are only finitely many regeneration times. Also, when there are infinitely many regeneration times, we show that for each $\varepsilon>0,$ the number of regeneration times in $[0,n]$ is no more than $(\log n)^{1+\varepsilon}$ as $n\rightarrow\infty.$

math.PR↗
arXiv2020

Asymptotics of product of nonnegative 2-by-2 matrices with applications to random walks with asymptotically zero drifts

Let $A_kA_{k-1}\cdots A_1$ be product of some nonnegative 2-by-2 matrices. In general, its elements are hard to evaluate. Under some conditions, we show that $\forall i,j\in\{1,2\},$ $(A_kA_{k-1}\cdots A_1)_{i,j}\sim c\varrho(A_k)\varrho(A_{k-1})\cdots \varrho(A_1)$ as $k\rightarrow\infty,$ where $\varrho(A_n)$ is the spectral radius of the matrix $A_n$ and $c\in(0,\infty)$ is some constant, so that the elements of $A_kA_{k-1}\cdots A_1$ can be estimated. As applications, consider the maxima of certain excursions of (2,1) and (1,2) random walks with asymptotically zero drifts. We get some delicate limit theories which are quite different from the ones of simple random walks. Limit theories of both the tail and critical tail sequences of continued fractions play important roles in our studies.

math.PR↗
arXiv2018

Orlicz-Besov imbedding and globally $n$-regular domains

Denote by $ {\bf\dot B}^{\alpha,\phi}(\Omega)$ the Orlicz-Besov space, where $\alpha\in\mathbb{R}$, $\phi$ is a Young function and $\Omega\subset\mathbb{R}^n$ is a domain. For $\alpha\in(-n,0)$ and optimal $\phi$, in this paper we characterize domains supporting the imbedding ${\bf\dot B}^{\alpha,\phi}(\Omega)$ into $ L^{n/|\alpha|}(\Omega)$ via globally $n$-regular domains. This extends the known characterizations for domains supporting the Besov imbedding ${\bf\dot B} ^s_{pp}(\Omega)$ into $ L^{np/(n-sp)}(\Omega)$ with $s\in(0,1)$ and $1\le p<n/s$. The proof of the imbedding ${\bf\dot B}^{\alpha,\phi}(\Omega)\to L^{n/|\alpha|}(\Omega)$ in globally $n$-regular domains $\Omega$ relies on a geometric inequality involving $\phi$ and $\Omega$ , which extends a known geometric inequality of Caffarelli et al.

math.FA↗