随机幂级数与指数级数

Random Power and Exponential Series

设已给概率空间,并且是这一空间上独立的复随机变量序列。随机幂级数或随机泰勒(Taylor)

The convergence, growth, natural boundary and the distribution of values of some random power seriesand random exponential seriesare studied, where {Xn(w)} is a sequence of complex independent random variables on the probability space (Q, A, ), , z and . We consider especially the case in which Xn(w) are symmetric and that in which Xn(w) = anZn(w), where {an} C and (Zn(w)} is a so-called N-sequence which contains Rademacher, Stein-haus and Gauss sequences as special cases. Some results of L. Arnold, R.E.A.C. Paley and A. Zygmund, J.-P. Kahane, J.E. Littlewood, A.C. Of ford, Sun Dao-chun, Liu Quan- sheng, the author and others are stated and some problems and related fields of mathematics are indicated .