| Project/Area Number |
09640285
|
|---|
| 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 | Nagoya City University |
|---|
Principal Investigator |
MISAWA Tetsuya Nagoya City Univ., Fact.of Economics, Associate Prof., 経済学部, 助教授 (10190620)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
HASHIMOTO Yoshiaki Nagoya City Univ., Inst.of Natural Sci., Prof., 自然科学研究教育センター, 教授 (50106259)
MIYAHARA Yoshio Nagoya City Univ., Fact.of Economics, Prof., 経済学部, 教授 (20106256)
SHIMIZU Akinobu Nagoya City Univ., Inst.of Natural Sci., Prof., 自然科学研究教育センター, 教授 (10015547)
|
|---|
| Project Period (FY) |
1997 – 1998
|
| Project Status |
Completed (Fiscal Year 1998)
|
| Budget Amount *help |
¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1998: ¥700,000 (Direct Cost: ¥700,000)
|
|---|
| Keywords | Stochastic dynamical systems / Conserved quantities and symmetry / Stochastic numerical analysis / Wavelet interpolation / Fleming-Viot processes / Mathematical finance / Stochastic analysis / Gevrey hypoellipticity / ウェーブレット関数補間 / 構造再現性 / 非線形マクロ動学 / Fleming-Viot過程 / wavelet解析 |
|---|
| Research Abstract |
This study is dealt with the stochastic difference schemes and related topics for stochastic dynamical systems governed by stochastic differential equations which have conserved quantities. The head investigator, T.Misawa, focuses on an one-dimensional stochastic Hamilton dynamical system in which the energy function (Hamiltonian) becomes a conserved quantity. For the system, he proposes two energy conservative stochastic difference schemes which leave Hamiltonians numerically invariant. and proves that the local error orders of accuracy of numerical solutions derived from the stochastic schemes are 2 and 4 respectively. Moreover, as a fundamental study for the thema, Nisawa also investigates on a method for deriving conserved quantities from symmetry in stochastic systems, the similarity method (a method of the reduction of the order of stochastic equations), and the relations between conserved quantities and symmetry in stochastic Hamilton systems.
As the related topics, Misawa treats the numerical simulations of a stochastic business cycle model in an open economy, a wavelet interpolation method with simulated annealing in time series analysis. A.Shimizu works with a genealogical problem of a stepping stone Fleming-Viot process and examines the fractional moments of the first returning time of positively recurrent Markov.chains. Y.Miyahara is concerned with stochastic analysisof the pricing problem of contingent claims ; he investigates on minimal entropy martingale measures of jump type price processes in incomplete assets markets. Y.Hashimoto deals with in the relation between positive-definite generalized functions and the heat kernel. Through the studies, we find out that stochastic numerical method is useful for the analysis of the several stochastic problems in such topics.
|
