講座題目：GTH Algorithm, Censored Markov Chains, and $RG$-Factorization in Block-Form

主講嘉賓：Yiqiang Q. Zhao

講座主持：王金亭 教授

講座時間：2025年9月12日（星期五）10：30-11：30

講座地點(diǎn)：中央財經(jīng)大學(xué)沙河校區(qū)二教113教室

講座摘要：

In 1985, Grassmann, Taksar and Heyman published their celebrated paper, in which a numerically stable algorithm was introduced for computing the stationary probabilities of a finite-state Markov chain. This algorithm later became the well-known GTH-algorithm (or the state-reduction method) in the literature, becoming one of the standard algorithms in applied probability. Later, in 1990, this algorithm was extended to dealing with stationary distributions of block-structured Markov chains with repeating rows by Grassmann and Heyman. In this talk, we first provide probabilistic interpretations of all components of the GTH-algorithm for the block-structured Markov chain. We then show that, in terms of the concept of censoring, the GTH-algorithm can be extended to infinite-state Markov chains. Finally, we demonstrate that the $RG$-factorization is analogous to LU-decomposition in Gaussian elimination, which is equivalent to the GTH-algorithm. It is worthwhile to note that the censored Markov chain produces a minimal error in approximating the stationary distribution for the original chain under the $l_1$-norm.

This talk is based on joint research with Qihui Bu.

嘉賓簡介：

趙以強(qiáng)博士是加拿大卡爾頓大學(xué)理學(xué)院終身正教授、卡爾頓-渥太華-魁北克大學(xué)統(tǒng)計概率聯(lián)合研究室主任。歷任卡爾頓大學(xué)數(shù)學(xué)統(tǒng)計學(xué)院院長、卡爾頓大學(xué)理學(xué)院副院長（主管科研及研究生工作）、渥太華-卡爾頓數(shù)學(xué)統(tǒng)計研究院主任、加拿大統(tǒng)計學(xué)會概率分會會長、加拿大運(yùn)籌學(xué)會溫尼伯分會會長、（國際著名）菲爾茲數(shù)學(xué)科學(xué)研究所董事會成員、英國劍橋大學(xué)牛頓學(xué)院訪問教授等。

趙教授主要從事應(yīng)用概率和隨機(jī)運(yùn)籌鄰域的研究，在國際一流權(quán)威期刊上發(fā)表了150多篇高水平的學(xué)術(shù)論文，其研究成果被國際同行廣泛引用(谷歌引用3000多次)，并得到高度評價，在應(yīng)用概率，尤其是排隊論及相關(guān)領(lǐng)域做出了重要的貢獻(xiàn)。趙以強(qiáng)教授連續(xù)30多年主持多項(xiàng)國家重要科研項(xiàng)目、現(xiàn)擔(dān)任五種國際主流權(quán)威期刊的副主編，包括OR Letters、Queueing Systems、Stochastic Models等。

主辦單位：管理科學(xué)與工程學(xué)院