吸収壁に到達するまでの試行数と原点通過回数の同時分布-城西大学.pdfVIP

/2014/12/7/ d d d d d p Po´lya urn sampling d d 1 p 1 q = 1 p 1 d, d + 1, . . . , 0, 1, . . . , d 1, d, d d d exchangeable sequence Feller 14 0, 1, . . . , z, . . . , a z 0 a 0 a 1, 1 ξ , ξ , . . . (iid) 1 2 P (ξi = 1) = p, P (ξi = 1) = q (1 p 1, q = 1 p ), i = 1, 2, . . . Xn = ξ1 + + ξn , X0 = 0 Xn , n = 0, 1, 2, . . . iid ξ , ξ , . . . exchangeable X , n = 0, 1, 2, . . . exchangeable sequence 1 2 n n (ξ , ξ , . . . , ξ ) ξ , ξ , . . . 1 2 n 1 2 exchangeable iid exchangeable Xn , n = 0, 1, 2, . . . P (Xn+1 = i + 1Xn = i) = p, P (Xn+1 = i 1Xn = i) = q = 1 p, 0 p 1 1 d 0 d d W N W = minn; Xn = d or Xn = d, N = number of m; Xm = 0 and 1 m W W N W N conditional joint pgf φ = E [tW sN X = i], for i = d + 1, ..., d 1. φ = φ . i 0 0  φ = ptφ + qtφ , (i = d + 2, ..., 2 or i = 2, ..., d 1)  i i+1 i−1    φ = ptsφ + qtφ  −1 −2  () :  φ = ptφ 1 + qtφ−1 φ = ptφ + qtsφ  1 2    φ = pt + qtφ