TY - JOUR ID - 1244 TI - A weak approximation for the Extrema's distributions of Levy processes JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Payandeh Najafabadi, A.T. AU - Kucerovsky, D.Z. AD - Department of Mathematical Sciences, Shahid Beheshti University, G.C. Evin, 1983963113, Tehran, Iran. AD - Department of Mathematics and Statistics, University of New Brunswick, Fredericton, N.B. Canada E3B 5A3. Y1 - 2017 PY - 2017 VL - 43 IS - 6 SP - 1867 EP - 1888 KW - Levy processes KW - positive-definite function KW - extrema's distributions KW - the Fourier transform KW - the Hilbert transform DO - N2 - Suppose that $X_{t}$ is a one-dimensional and real-valued L\'evy process started from $X_0=0$, which ({\bf 1}) its nonnegative jumps measure $\nu$ satisfying $\int_{\Bbb R}\min\{1,x^2\}\nu(dx)<\infty$ and ({\bf 2}) its stopping time $\tau(q)$ is either a geometric or an exponential distribution with parameter $q$ independent of $X_t$ and $\tau(0)=\infty.$ This article employs the Wiener-Hopf Factorization (WHF) to find, an $L^{p^*}({\Bbb R})$ (where $1/{p^*}+1/p=1$ and $1