A general result on r-quick convergence for time-averages of regenerative stochastic processes is derived and then applied to Markov processes. The notion of r-quick convergence was used by Lai (1981) to show asymptotic optimality of invariant sequential probability ratio tests. In the last...

For an extremal process (Zt)t the optimal stopping problem for Xt = f(Zt)-g(t) gives the continuous time analogue of the optimal stopping problem for max{Y1,...,Yk}-ck where Y1, Y2,... are i.i.d. For the continuous time problem we derive optimal stopping times in explicit form and also show that...

We treat the problem of finding asymptotic expansions for the variance of stopping times for Wiener processes with positive drift (continuous time case) as well as sums of i.i.d. random variables with positive mean (discrete time case). Carrying over the setting of nonlinear renewal theory to...

For a continuous time stochastic process with distribution P[theta] depending on a one-dimensional parameter [theta] the problem of sequentially testing [theta] = 0 against [theta] 0 is treated. We assume that the process of likelihood ratios has a certain representation which allows to obtain...