Numerical Evaluation of Path Integrals

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We have formulated a path integral theory on the basis of a mathe-matical theorem. We have presented not only the formalism but also the practical method of numerical evaluation of path integrals. As was explicitly shown, our method gives satisfactory results for a nonlinear diffusion process as well as for a linear relaxation process. Usefulness of our theory will be further clarified when we apply the method to unsolved problems in statistical physics and other area of re-searches (for instance, the communication theory or the theoretical biology). These are left for our future study.

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