Study of infinite dimensional stochastic analysis and stochastic numerical analysis

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Results in infinite dimensional stochastic analysisSUGITA and TANIGUCHI investigated the oscillatory integrals on an abstract Wiener space and got the following result Let the phase function be a double Wiener integral and let the amplitude function be a multiple Wiener integral. If it is impossible to define properly the value of the amplitude function at the origin, the behavior of the oscillatory integral becomes quite different from finite dimensional cases.SUGITA and TAKANOBU got the following result Let {f^<(m)>}_m be a sequence of symmetric statistics of m variables. Then the sequence of random variables {f^<(m)>(chi+nalpha)}_n on the *-dimensional torus converges as m * * to the i.i.d. of multile Wiener intgerals.Results in stochastic numerical analysisFrom Jan.27 to Jan.30, we held a reseach conference "Probability theorey and computational mathematics" at Kyushu University. SUGITA gave a talk there with title "Pseudorandom number generation by means of irrational rotation-Fourier series approach". From Nov.9 to Nov.11, we held a research conference "The theory and methods of stochastic numerical analysis" at Kanazawa university. SUGITA gave a talk there with title "Robustness of quasi-Monte Carlo methods".