1987 Fiscal Year Final Research Report Summary
Research of Stochastic Analysis
| Project/Area Number |
61540162
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyushu University |
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Principal Investigator |
WATANABE Hisao Professor at Faculty of Engineering, Kyushu University, 工学部, 教授 (40037677)
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| Co-Investigator(Kenkyū-buntansha) |
SUZUKI Masakazu Associate Professor at Faculty of Engineering, Kyushu University, 工学部, 助教授 (20112302)
YOSHIKAWA Atsushi Professor at Faculty of Engineering, Kyushu University, 工学部, 教授 (80001866)
NISHINO Toshio Professor at Faculty of Engineering, Kyushu University, 工学部, 教授 (30025259)
TANIGUCHI Setsuo Assistant Professor at Faculty of Engineering, Kyushu University, 工学部, 講師 (70155208)
KUNITA Hiroshi Professor at Faculty of Engineering, Kyushu University, 工学部, 教授 (30022552)
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| Project Period (FY) |
1986 – 1987
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| Keywords | Diffusion approximations / Stochastic difference equations / Martingale methods / Perturbation methods / Stochastic partial differential equation / ランダムな係数をもつ放物型偏微分方程式 |
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| Research Abstract |
1. Diffusion approximations of some stochastic difference equations
In this paper, we consider the diffusion approximations of some stochastic processes with discrete parameter which are asymptotically given by stochastic difference equations. We prove it by Martingale methods and improve the previous results.
2. On the convergence of partial differential equations of parabolic type with rapidly oscillating coefficients to stochastic partial differential equations
In this paper, we consider on the convergence of partial differential equations of parabolic type with rapidly oscillating coefficients to stochastic partial differential equations. We use the martingale methods and the functinal method to prove uniqueness of martingale problem. Our emphasis is in treating with strongly mixing noises.
3. Convergence of stochastic flows connected with stochastic ordinary differential equations
The systematic study of the limiting theorem of stochastic dynamical systems defined by stochastic differential equations. By this study we have the unified approach of the following problem which have been studied individually. (1) Approximation theorem of stochastic differential equations. (2) Asymptotic behavior of solutions of stochastic ordianry differential equation with strong mixing property. (3) Limit theorem of the driven process by Papanicolaou-Stroock-Varadhan.
4. A stochastic approach to the Siloc boundary
When a bounded domain is characterized by a suitable family of plurisubharmonic functions, we showed that its Silov boundary is contained in a subset of the boundary obtained from the family. Moreover, we applied this observation to the investigation of the minimum principle for the complex Monge-Ampere operator.
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