Stochastic Numerical Analysis of Nonlinear Diffusions

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In this research plan we have mainly concerned with the theoretical study of those problems (eg. construction of the stochastic model, study on the influence of the quality of random numbers to the simulation scheme, etc), that can arrise in the development of probabilistic simulation schemes of nonlinear diffusion phenomena.Among those nonlinear phenomena we picked up some typical problems in mathematicasl physics, such as ; (A) Reaction-Diffusion system, and (B) Motion of Nonlinear fluids , and we aimed to establish the model of many-particles system to those phenomena and to develop efficient probabilistic simulation methods based on our stochastic (SDE, SPDE) models.Through the research activities of two years period, we have got many interesting and important results, theoretical and practical in both senses. Most of them have been or going to be published in appropriate journals, while they have been also presented in Conferences or Workshops, international or domestic. Some of the publications (ie. re- or pre-prints of the articles as well as the abstracts of the conferences) are attached to the report of this research plan. Besides we have also made a contribution to this research domain by organizing two domestic Conferences, one at Kyushuu Univ. in Jan.of 1998, and another is at Kanazawa Univ. in Nov.of 1998 (both have been held with the colaboration of Prof H.Sugita of Kyushuu Univ).