1997 Fiscal Year Final Research Report Summary
STUDY OF SELF-SIMILAR PROCESSES
| Project/Area Number |
08454038
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | OCHANOMIZU UNIVERSITY |
|---|
Principal Investigator |
KASAHARA Yuji OCHANOMIZU UNIVERSITY FUCULTY OF SCIENCE,PROFESSOR., 理学部, 教授 (60108975)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
NARITA Kiyoko OCHANOMIZU UNIVERSITY FUCULTY OF SCIENCE,RESEARCH ASISTANT, 理学部, 助手 (80189208)
MATSUZAKI Katsuhiko OCHANOMIZU UNIVERSITY FUCULTY OF SCIENCE,ASSOC.PROFESSOR, 理学部, 助教授 (80222298)
YOSHIDA Hiroaki OCHANOMIZU UNIVERSITY FUCULTY OF SCIENCE,ASSOC.PROFESSOR, 理学部, 助教授 (10220667)
KANEKO Akira OCHANOMIZU UNIVERSITY FUCULTY OF SCIENCE,PROFESSOR, 理学部, 教授 (30011654)
TAKEO Fukiko OCHANOMIZU UNIVERSITY FUCULTY OF SCIENCE,PROFESSOR, 理学部, 教授 (40109228)
|
|---|
| Project Period (FY) |
1996 – 1997
|
| Keywords | self-similar / fractional Brownian motion / extremal process / local time / Gaussian process / occupation times / limit theorem |
|---|
| Research Abstract |
・We studied the limiting processes for occupation times of fractional Brownian motion, which is a typical self-similar stochastic process. We see that the limiting process degenerates with the usual linear normalization but if consider the processes with the log-scale, we do have a meaningful process, which is the inverse of the so-called extremal process.
・We generalized the above result to a certain class of Gaussian processes, where the occupation time increases slowly.
・We studied the asymptotic behavior of the local times of fractional Brownian motion. As the index times the dimension approaches 1, we see that the one-dimensional marginal distributions of the local time at the origin converge to the exponentioal distribution, and furthermore, the processes, with a suitable time scale, converge to the inverse extremal process.
・The invariant set under a family of functions has self-similarity. We studied its topological aspects.
|
