Let {Xn, n=1} be a sequences of i.i.d. random variables with survival function F(x)=P[X1>x] . A wavelet linear survival function n F(x) based on X1, X2,…, Xn is introduced as an estimator for n F(x) . We establish that the Lp’ -loss (2=r=p¢= ¥) of the linear wavelet survival function estimator for a stochastic processes convergence at the rate rs n2 s 1(s s 1/p 1 / p ) - ¢ ¢+ ¢= - + ¢ when the survival function, n F(x) belongs to the Besov space s p,q B . Strong consistency and pointwise as well as uniform of n F(x) are discussed.

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