1998 Fiscal Year Final Research Report Summary
Study of recurrence property of jump type Markov processes
| Project/Area Number |
09640283
|
|---|
| 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 | UNIVERSITY OF THE RYUKYUS |
|---|
Principal Investigator |
YAMAZATO Makoto University of the Ryukyus, Dept.of Mathematical Sciences, Professor -> 琉球大学, 理学部, 教授 (00015900)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
CHEN Chunhang University of the Ryukyus, Dept.of Mathematical Sciences, Associate Professor, 理学部, 助教授 (00264466)
HENNA Jogi University of the Ryukyus, Dept.of Mathematical Sciences, Professor, 理学部, 教授 (80045195)
NISHISHIRAHO Toshihiko University of the Ryukyus, Dept.of Mathematical Sciences, Professor, 理学部, 教授 (70044956)
|
|---|
| Project Period (FY) |
1997 – 1998
|
| Keywords | storage process / OU type process / Levy measure / recurrence |
|---|
| Research Abstract |
Let {A(t)} be a nonnegative subordinator without drift and r be a left continuous function on the nonnegative line to the nonnegative line with positive right limits satisfying r(O) = 0 and r(x) > 0 for x > 0. We say that a stochastic process {X(t)) is a storage process if it is determined by a stochastic differential equation
dX(t) = -r(X(t))dt + dA(t)
The following are our results : (a) A semigroup corresponding to the storage process is strongly continuous on the Basnach space consisting of bounded continuous functions on the nonnegative line vanishing at infinity if (I) an integral of 1/r(x) near infinity is divergent and (2) the total mass of the Levy measure is finite or the function r is nondecreasing. We determined the domain of the generator in the Case the total mass of the Levy measure is finite and gave a core for the generator in case the function r is nondecreasing. (b) We showed that the storage process is either positive recurrent or null recurrent or transient and obtained a sufficient condition for the process to be transient and a sufficient condition for the process to be recurrent. It should be remarked that 'we assume neither finiteness of the total mass of the Levy measure nor nondecreasingness of r. There are cases for which these two conditions can not be applied. However, we showed that in special case that the process Is a process of Ornstein-Uhlenbeck type, a part of the above mentioned sufficient condition for transience is sufficient for transience and it is also necessary.
|
Research Products
(12 results)
