| Summary: | 碩士 === 輔仁大學 === 數學系碩士班 === 102 === The purpose of the thesis is to investigate some properties of a long-range random walk on Z^d which is 1-step distribution D(x) has symmetry and the rate of decay is order |x|^(−α−d) as |x| → ∞ for some α > 0 and d > 0. The first result, we discuss the asymptotic behavior of the gyration radius of order r where 0 < r < α and α > 2. Furthermore we obtain the main coefficient as fixed one xj-axis direction for j = 1, 2, ..., d. The second result, we discuss the recurrence or transient for the long-range random walk with α > 0 and dimension d > 0. The proof is basic on Fourier transform and fractional derivative.
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