| Budget Amount *help |
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1998: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1997: ¥900,000 (Direct Cost: ¥900,000)
|
|---|
| Research Abstract |
In this research, a certain type of stochastic differential equations (SDE's) based on C(R^d, R^d) valued sernimartingales, which will be called to be canonical, are investigated and the following results are obtained. Here, C(Rd, Rd) denotes the space of continuous mappings from the d-dimensional Euclidean space Rd to itself.
(1) The definition of canonical integrals based on C(R^d, R^d) valued semimartingales as a class of stochastic integrals and the relationship to the Ito integrals and the Stratonovich integrals.
(2) The existence and uniqueness of the solutions of canonical SDE's.
(3) Homeomorphic and moreover diffeomorphic properties of the solutions.
(4) A fact that the inverse of the stochastic flow of diffeomorphisrns generated by a canonical SDE is represented as a system of solutions of the corresponding backward canonical SDE under some suitable conditions.
Through this research, it is shown that by their own structure canonical SDE's naturally generate several nice properties in relation to the theory of stochastic flows.
These results were reported at a symposium of the Mathematical Society of Japan in September 1998. Furthermore, the details will be published in Kyushu Journal of Mathematics as a pair of papers written by the head investigator and Professor Hiroshi Kunita.
|
