Study of infinite dimensional stochastic analysis and stochastic numerical analysis

在无限维随机分析中，issugita和TANIGUCHI研究了抽象Wiener空间上的振荡积分，得到如下结果：设相函数为二重Wiener积分，设幅函数为多重Wiener积分。如果不可能在原点正确地定义振幅函数的值，那么振荡积分的行为就会与有限维情况大不相同。SUGITA和TAKANOBU得到如下结果设{f^<(m)>}_m是m个变量的对称统计量序列。则在*维环面上的随机变量序列{f^<(m)>(chi+n α)}_n以m * *收敛于多个Wiener积分的i.i.d。1月27日至1月30日，我们在九州大学召开了“概率论与计算数学”的研究会议。杉田在那里做了一个题为“用无理性旋转-傅立叶级数方法生成伪随机数”的演讲。11月9日至11日，我们在金泽大学召开了“随机数值分析的理论与方法”研究会议。杉田在那里做了题为“拟蒙特卡罗方法的鲁棒性”的演讲。

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".