Statistical asymptotic theory for stochastic processes And its computer implementation

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The higher-order asymptotic expansions of many test statistics for stochastic processes are obtained, which leads to asymptotic expansion formulas of test statistics for diffusion processes. Highly accurate approximation formulas for major discriminant functions are derived in case of small or ergodic diffusion observations. Moreover, asymptotic expansions of marked point processes with time in-homogenous intensity functions are obtained, and using the mathematical formula manipulation, explicit expression of the coefficients in the expansions are given. Computer program for the approximation formulas obtained are coded, and their accuracy is measured numerically.