數學研究所
You are here:   首頁   ⇒   人員   ⇒   合聘及退休研究人員   ⇒   姜祖恕

退休研究人員 |   姜祖恕

 



聯絡資訊
  • Email : matsch AT math.sinica.edu.tw
  • Phone:+886 2 2368-5999 ext. 739
  • Fax:    +886 2 2368-9771
  相關連結

學歷
  • Ph.D. The University of Minnisota (1980)
  • M.S. 美國威斯康辛大學密爾瓦基分校 (1975)
  • B.S. 台灣大學 (1972)
  研究專長
  • 機率論

經歷
  • visiting member University of North Carolina 1989 - 1991
  • Research Fellow Institute of Mathematics, Academia Sinica, R.O.C. 1986 - Present
  • Visiting associate professor University of Minnisota 1985 -1986
  • Associate Research Fellow Institute of Mathematics, Academia Sinica, R.O.C. 1981 - 1986
  • Assistant Professor University of Wisconsin-Milwaukee 1980 - 1981

研究簡介

The major interest of Dr. Chiang's are Probability theory, Stochastic processes and especially, their applications to Statistics and Mathematical Analysis.

 For the system of $d-$dimesnional stochastic differential equations, $d\ge 2$,
$$ \begin{array}{ll} & dX_t^{\epsilon} =b(X_t^{\epsilon})dt+\epsilon dW_t,\ \ \ \ t\in [0,T]\\ & X_0^\epsilon = x \in H\subseteq R^d, \end{array} $$

 where $b(x)=(b_1(x),...,b_d(x))$ is a bounded smooth vector field except along the hyperplane $H=\{ x\in R^d, x_1=0\}$ but satisfies the stability condition in the sense that there exists a constants $c>0$ such that for some $\delta_0>0$ $b_1(x)\le -c$ if $x_1\in (0,\delta_0)$ and $b_1(x)\ge c$ if $x_1\in (-\delta_0,0)$, we shall prove that the central limit theorem holds for $(X^\epsilon (\cdot), u^{\epsilon+}(\cdot))$ where $u^{\epsilon+}_t$ is the  occupation time of $X^\epsilon(t)$ in the right half space $H^+=\{ x\in R^d, x_1>0\}$ up to time $t$. To be explicit, we shall show that there exist two continuous functions $\phi (\cdot) \in C([0,T],R^d)$ and $\psi(\cdot)\in C([0,T],R)$ such that  the process $(\frac{1}{\epsilon}(X^\epsilon(\cdot)-\phi(\cdot)), \frac{1}{\epsilon}(u^{\epsilon+}{(\cdot)}-\psi(\cdot)))$ converges  to a Gaussian proess in $C([0,T],R^{d+1})$ in probability  thus in distribution as $\epsilon\to 0$.


部分著作目錄 List ↓

中央研究院數學研究所版權所有 隱私權及安全政策     |  與我們聯絡  |    Latest Update:2017-11-13
(台大院區)總機:886-2-23685999  傳真機:02-23689771 (行政室) 數學所同仁 電話分機 總表  
Skype Account : mathvoip        地址:台北市10617羅斯福路四段1號 天文數學館6樓 (中央研究院數學所)
建議使用 Chrome, Firefox, Microsoft IE 10.0 以上版本觀看,並設定 1024X768 解析度以獲最佳瀏覽效果。