2026年度より、静岡大学工学部共通講座会議・数学教室では、 解析学に関連する分野の研究交流の場として 「浜松解析セミナー」を立ち上げました。
静岡大学浜松キャンパスにて不定期に開催しますが、開催曜日は木曜日とし、約1時間半のセミナーを予定しております。
皆様のご参加を心よりお待ち申し上げます。
会場：静岡大学浜松キャンパス 総合研究棟2階 総22教室
講演者：Ju-Yi Yen 氏 (University of Cincinnati, USA)
題目：Limit Theorems for Additive Functionals of Recurrent Markov Processes
要旨：Additive functionals arise naturally when studying the accumulated behavior of stochastic processes, with occupation times being a fundamental example. For positive recurrent Markov processes, their long-time behavior is often described by classical ergodic theorems and central limit theorems. However, the situation is different for null recurrent processes, where the invariant measure is infinite and the usual normalization by time is no longer appropriate.
In this talk, I will discuss how local time and excursion theory provide a framework for studying the asymptotic behavior of additive functionals of recurrent processes. Starting with Brownian motion, I will explain how inverse local time leads to a regenerative structure and how Ray–Knight theorems help us understand the fluctuations of additive functionals. I will then discuss extensions to symmetric stable processes, one-dimensional diffusions, and more general symmetric Markov processes.
The talk will focus on the main ideas and connections between these results, with an emphasis on the probabilistic intuition rather than technical proofs.
星賀 彰 足達 慎二 赤堀 公史 中島 徹 藤嶋 陽平 村田 美帆 谷口 晃一
谷口 晃一 (taniguchi.kohichi [at] shizuoka.ac.jp)
村田 美帆 (murata.miho [at] shizuoka.ac.jp)
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