2000 Fiscal Year Final Research Report Summary
A RESEARCH OF STOCHASTIC PROCESSES IN RANDOM ENVIRONMENT
| Project/Area Number |
11640122
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | YAMAGUCHI UNIVERSITY |
|---|
Principal Investigator |
KAWAZU Kiyoshi EDUCATION, YAMAGUCHI UNIVERSITY PROFESSOR, 教育学部, 教授 (70037258)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
YANAGI Kenjirou TECHNOLOGY, YAMAGUCHI UNIVERSITY PROFESSOR, 工学部, 教授 (90108267)
KURIYAMA Ken TECHNOLOGY, YAMAGUCHI UNIVERSITY PROFESSOR, 工学部, 教授 (10116717)
OKADA Mari TECHNOLOGY, YAMAGUCHI UNIVERSITY ASOC.PROFESSOR, 工学部, 助教授 (40201389)
WATANABE Tadasi EDUCATION, YAMAGUCHI UNIVERSITY PROFESSOR, 教育学部, 教授 (10107724)
KASAI Siniti EDUCATION, YAMAGUCHI UNIVERSITY LECTURER, 教育学部, 講師 (40224373)
|
|---|
| Project Period (FY) |
1999 – 2000
|
| Keywords | random environment / Brownian motion / diffusion process / one-sided potential / limit distribution |
|---|
| Research Abstract |
Let W be the set of continuous functions on a real line which vanishes identically on [0, ∞) and introduce the Wiener measure on W.Let {X (t), t【greater than or equal】 0} be a stochastic process which is a diffusion process defined by the sacale function ∫^x_0 exp {w (y)} dy and the speed measure 2 exp {-w (x) } dx (w ∈ W) in the random environment w. Then our results are as follows ;
(i) As t→∞, t^<-1/2>X (t) has the limit distribution such that <<numerical formula>> whose support is [0, ∞).
(ii)<<numerical formula>>
(iii)(logt)^<-2> min_<0【less than or equal】s【less than or equal】t>X (s) converges in distribution to {M, P}. Here, -M has the law of the first leavung time from [0, 2] of the one-dimensional Brownianmotion starting from 1/2.
|
