第21回デリバティブ研究部会セミナー

投稿日: 2023/12/30 21:08

日時：2023年8月26日（土曜）10:00-11:00am

場所：立命館大学東京キャンパス(東京駅日本橋駅口徒歩１分サピアタワー８F）&zoom (いずれの場合でもがこちら から参加登録が必要です）

講師：Ju-Yi YEN （University of Cincinnati）

題目： Excursion approach to central limit theorem for some null recurrent diffusion processes

概要: We consider limits of  the additive functional of  a recurrent diffusion process $X$. Note that if $X$ is positive recurrent  with stationary distribution $\pi$, the ergodic theorem and central limit theorem are well-known results; in particular,  the time average $\frac{1}{T} \int_{0}^{T} f(X_{s}) ds$ converges to the space average $\int_{\mathbb{R}} f(x) \pi(x) dx$. However, this property fails when $X$ is a null recurrent linear diffusion. Instead of averaging the additive functional by $T$, we reconfirm some classical results that the local time process of $X$ is the proper scale to the additive functional in order to obtain the corresponding limit theorems. The main result of this work is to prove the central limit theorem for some null recurrent linear diffusion processes. The gist of our proofs is to use the Brownian excursion theory to achieve the random time change.