컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0475 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Probability / Stochastic Process / Statistics (SS-12) |
| 영문제목 (Title(Eng.)) |
Evaluation formulas for generalized conditional Wiener integrals on a function space |
| 저자(Author(s)) |
Dong Hyun Cho1 Kyonggi University1 |
| 초록본문(Abstract) | Let $C[0,t]$ denote the space of real-valued continuous functions on the interval $[0,t]$ and let $h\in L_2[0,t]$ with $h\neq 0 $ a.e. on $[0,t]$. Define a stochastic process $Z: C[0,t]\times [0,t]\to \mathbb R$ by \begin{eqnarray*} Z(x,s)=\int_0^s h(u) dx(u) \end{eqnarray*} for $x\in C[0,t]$ and $s\in[0,t]$. For a partition $0 < t_1 < \cdots < t_n=t$ of $[0,t]$, let \begin{eqnarray*} X_n(x) = (Z(x,t_1),\cdots, Z(x,t_n)). \end{eqnarray*} In this talk, with the conditioning function $X_n$, we derive a simple formula for generalized conditional Wiener integrals of functions defined on $C[0,t]$ which is a probability space and a generalization of the Wiener space. As applications of the formula, we evaluate the generalized conditional Wiener integrals of functions of the forms \begin{eqnarray*} \int_0^t (Z(x,s))^m ds \ ( m\in\mathbb N) \text{ and } Z(x, t_1)Z(x,t_2) \end{eqnarray*} for $x\in C[0, t]$. |
| 분류기호 (MSC number(s)) |
28C20 |
| 키워드(Keyword(s)) | analogue of Wiener measure, conditional Wiener integral, simple formula for conditional Wiener integrals |
| 강연 형태 (Language of Session (Talk)) |
English |