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