| Co-Investigator(Kenkyū-buntansha) |
OKAZAKI Yoshiaki Kyushu Inst.Tech.(Fac.of Information), Prof., 情報工学部, 教授 (40037297)
SUGITA Hiroshi Kyushu Univ.(Fac.of Mathematics) Assoc.Prof, 大学院・数理学研究院, 助教授 (50192125)
TANIGUCHI Setsuo Kyushu Univ.(Fac.of Mathematics) Assoc.Prof., 大学院・数理学研究院, 助教授 (70155208)
AIDA Shigeki Osaka Univ.(Fac.of Fund.Tech.) Assoc.Prof., 大学院・基礎工学研究科, 助教授 (90222455)
SHIGEKAWA Ichiro Kyoto Univ.(Fac.of Science) Prof., 大学院・理学研究科, 教授 (00127234)
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| Research Abstract |
Absolute Continuity of a Random Translation. Let G = {G_k} be a standard Gaussian sequence, Y = {Y_k} be an independent random sequence which is also independent of G.We gave necessary and sufficient conditions for μ_G 〜 μ_G+Y (mutually absolutely continuous) when each Y_k has symmetric three values.
G measure. We proved that two probability measures on a Polish space which have quasi-invariant and ergodic actions are mutually absolutely continuous or singular. This dichotomy includes that of G-measures as a special case.
Asymptotic Estimations of Stochastic Oscillatory Integrals. We have obtained several results on the asymptotic estimations of stochastic oscillatory integrals I (λ ; q, Ψ) on an abstract Wiener space as |λ|→ ∞ under hypothesis on the phase function q and the oscillation function Ψ. Among those are the exponential decay, the principle of the stationary phase, a complex transformation of the Wiener measure based on the Jacobi equation, the localisation, etc..
Stochastic An
… More
alysis on the Path Space Analysing the path space on a Riemannian manifold, we obtained the short time estimation of Varadhan type of an infinite dimensional diffusion, the existense and the estimation of the spectral gap, and fine estimations of the heat kernel, etc..
Harmonic Analysis of a Fractal. We have expressed the Sierpinski gasket as a Martin boundary of a certain Markov chain, proved that the harmonic measure coincides with the canonical Hausdorff measure, compared the Mrtin metric with the Euclidean one explicitly.
Absolute Continuity of a Random Translation. Let G = {G_k} be a standard Gaussian sequence, Y = {Y_A} be an independent random sequence which is also independent of G.We gave necessary and sufficient conditions for μ_G 〜 μ_G+Y (mutually absolutely continuous) when each Y_k has symmetric three values.
G measure. We proved that two probability. measure on a Polisla space which have quasi-invariant and ergodic actions are mutually absolutely continuous or singular. This dichotomy includes that of G-measures as a special case.
Asymptotic Estimations of Stochastic Oscillatory Integrals. We have obtained several results on the asymptotic estimations of stochastic oscillatory integrals I (λ ; q, Ψ) on an abstract Wiener space as |λ|→ ∞ under hypothesis on the phase function q and the oscillation function Ψ. Among those are the exponential decay, the principle of the stationary phase, a complex transformation of the Wiener measure based on the Jacobi equation, the localisation, etc..
Stochastic Analysis on the Path Space Analysing the path space on a Riemannian manifold, we obtained the short time estimation of Varadhan type of an infinite dimensional diffusion, the existense and the estimation of the spectral gap, and fine estimations of the heat kernel, etc..
Harmonic Analysis of a Fractal. We have expressed the Sierpinski gasket as a Martin boundary of a certain Markov chain, proved that the harmonic measure coincides with the canonical Hausdorff measure, compared the Mrtin metric with the Euclidean one explicitly. Less
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