Probability theory related to analysis and geometry

召开了以下专题讨论会，进行了会谈和讨论，取得了丰硕成果。“概率论与计算机数学”：我们与物理学和工程学领域的几位研究人员一起，从理论和应用的角度探讨了这一主题。其中，Sugita提出了一种利用动力学方法产生伪随机数的新方法，Fukuyama讨论了用这种随机数产生伪随机数的Monte Carlo方法的收敛性，Takashima报道了将伪随机数看作随机过程的检验.“随机控制专题”：在本研究中，揭示了在风险敏感随机控制问题中，当随机控制过程是稳定的情况下，避免崩溃的条件比以前已知的要宽松得多.“量子混沌的概率论专题2”：讨论量子混沌的数学问题，如量子数的混沌 ...更多信息 r理论或量子混沌在随机分析中的应用.“随机分析和几何”：金井正彦介绍了离散群作用刚性的新方法，K.D.Elworthy从随机微分方程的角度讨论了同调和同伦消失定理，浦川一介绍了他的图的谱几何。Hironori Kumura讨论了黎曼流形的本质谱的结构，Atsushi Kasue对黎曼浸没的几何分析.“群体遗传学中的随机过程”：在S.N. Chelier和Tachida参加的研讨会的讨论中，给出了太田-Tanchida的纸牌屋模型的数学公式和研究主题。6.“非平衡统计力学和概率论”：随着H.Spohn（路德维希-马克西米利安大学）的密集讲座。和Kyoji川崎（中部大学）和其他一些概率学家的谈话，分析了非平衡态统计力学与概率论关系的现状和未来的前景.“关于扩散过程和随机游动的若干问题”：主要对布朗运动局部时的新结果和扩散过程的综述进行了讨论.“随机分析与渐近理论”：对随机渐近理论进行了大量的讨论和讨论。不仅包括已经建立的渐近展开式和大偏差原理（拉普拉斯方法），而且还包括随机振荡积分的渐近理论，其未来的发展是很有希望的。少

The following symposiums were held, where talks and discussions were given with fruitful results.1."Probability Theory and Computor Mathematics" : With several researchers in the field of physics and engineering, we approached to the topics both from theoritical and applicative point of view. Among all, Sugita proposed a new method of generating pseudo-random numbers by means of dynamics, Fukuyama discussed on the convergence of the Monte Carlo method with this random numbers, and Takashima reported on the test in which the pseudo-random numbers are regarded as a stochastic proccess.2."Topics on Stochastic Control" : In this research, it was revealed that the condition for avoiding break down in the risk sensitive stochastic control problem can be much relaxd than was known before in the case when the stochastic control processes are stable.3."Topics on Probability Theory for Quantum Chaos 2" : Talks and discussions on mathematical aspect of quantum chaos such as quantum chaos in numbe … More r theory or quantum chaos in stochastic analysis were given.4."Stochastic analysis and geometry" : Masahiko Kanai introduced a new approach to the rigidity of discrete group action, K.D.Elworthy discussed on the homology and homotopy vanishing theorems from the point of view of stochastic differential equations and Hajime Urakawa introduced his spectral geometry of graphs. Hironori Kumura discussed the structure of esential spectre for Riemannian manifold, and Atsushi Kasue geometric analysis of Riemannian submersions.5."Stochastic Processes in Population Genetics" : In the discussion of this symposium, in which S.N.Ethier and Tachida participate, the mathematical formulation of the model and research subject for House-of-Cards model due to Ohta-Tanchida was given.6."Non-equilibrium Statistical Mechanics and Probability Theory" : With the intensive lectures of H.Spohn (Ludwig-Maximilians-Univ.) and Kyoji Kawasaki (Chubu Univ.) and talks of some other probabilists, the present situations and prospect in the furture for therelation of non-equilibrium statistical mechanics and probability theory was analyzed.7."Some topics on Diffusion Processes and Random Walks" : Talks and discussion mainly on new results on the local time of Brownian motions and survey on diffusion processes were given.8."Stochastic Analysis and Asymptotics Theory" : Many talks and discussions on stochastic asymptotics theory were given. They covered not only the already established asymptotic expansions and large deviation priciple (Laplace method), but also the aymptotics theory on stochastic oscilatory integral, whose future development is strongly expected. Less