Studies on diffusion processes and fuzzy valued stochastic analysis

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In this study, we first found a lot of new type of stochastic processes in the class of one-dimensional continuous stochastic process with Markov property but without strong Markov property, and moreover determined that class. We then extended strong laws of large numbers and derived large deviation principle for fuzzy set valued random variables. In addition, we proved the existence and uniqueness of solutions almost surely in the space of fuzzy sets (resp. sets) to stochastic differential equations with fuzzy sets (resp. sets) coefficients. We also estimated the term with power 3 integrand in the asymptotic expansion in perturbative Chern-Simons theory. A new characterization of the two-parameter Poisson-Dirichlet distribution was given.