| Budget Amount *help |
¥7,450,000 (Direct Cost: ¥6,100,000、Indirect Cost: ¥1,350,000)
Fiscal Year 2009: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2008: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2007: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2006: ¥1,600,000 (Direct Cost: ¥1,600,000)
|
|---|
| Research Abstract |
A deep study of the theory of Stochastic Calculus was made, aiming to apply stochastic oscillatory integrals to the KdV equation and the KdV hierarchy. Several new results in Stochastic Calculus are obtained : an application of stochastic representation to the convergence of reflectionless potentials, concrete expression of stochastic oscillatory integral, a Wiener integral representation approach to non commutative harmonic oscillator. Moreover, a new Wiener functional of the Brownian sheet was investigated. Finally, the relationship between stochastic oscillatory integrals and Jacobi equations was studied to understand stochastic oscillatory integrals from the point of view of algebraic analysis.
|
