2009 Fiscal Year Final Research Report
Studies on diffusion processes and fuzzy valued stochastic analysis
| Project/Area Number |
19540140
|
|---|
| 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 | Saga University |
|---|
Principal Investigator |
OGURA Yukio Saga University, 理工学部, 非常勤講師 (00037847)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
MITOMA Itaru 佐賀大学, 理工学部, 教授 (40112289)
HANDA Kenji 佐賀大学, 理工学部, 准教授 (10238214)
|
|---|
| Project Period (FY) |
2007 – 2009
|
| Keywords | 拡散過程 / マルコフ性 / ファジィ集合値確率変数 / 集合係数の確率微分方程式 / 大偏差原理 / Chern-Simons理論 / Poisson-Dirichlet分布 |
|---|
| Research Abstract |
In this study, we first found a lot of new type of stochastic processes in the class of one-dimensional continuous stochastic process with Markov property but without strong Markov property, and moreover determined that class. We then extended strong laws of large numbers and derived large deviation principle for fuzzy set valued random variables. In addition, we proved the existence and uniqueness of solutions almost surely in the space of fuzzy sets (resp. sets) to stochastic differential equations with fuzzy sets (resp. sets) coefficients. We also estimated the term with power 3 integrand in the asymptotic expansion in perturbative Chern-Simons theory. A new characterization of the two-parameter Poisson-Dirichlet distribution was given.
|
