This paper presents a criterion for stopping non-linear iterative algorithms, specifically the Richardson-Lucy algorithm that is widely used to restore images from the Hubble Space Telescope. The criterion is based on generalized cross-validation and is also computed iteratively. We will present examples displaying the power of the stopping rule, and will discuss the abilities and shortcomings ...

This paper studies an optimal stopping time problem for pricing perpetual American put options in a regime switching model. An explicit optimal stopping rule and the corresponding value function in a closed form are obtained using the “modified smooth fit” technique. The solution is then compared with the numerical results obtained via a dynamic programming approach and also with a two-point bo...

It is shown that, in order that the multiplicativity rule W b aW c b = W c a , which essentially characterises Weyl processes, continue to hold when the sure times a < b < c are replaced by stop times, it is sufficient to use left stopping at the lower limit a and right stopping at the upper limit b in W b a . . Dedicated to Zhiyuan Huang on his 75th birthday. MSC Classification 81S25.

A version of the dynamical systems method (DSM) for solving ill-conditioned linear algebraic systems is studied. An a priori and an a posteriori stopping rules are justified. An iterative scheme is constructed for solving ill-conditioned linear algebraic systems.

Let Xn, . . . , X1 be i.i.d. random variables with distribution function F and finite expectation. A statistician, knowing F , observes the X values sequentially and is given two chances to choose X’s using stopping rules. The statistician’s goal is to select a value of X as large as possible. Let V 2 n equal the expectation of the larger of the two values chosen by the statistician when procee...

The full-information secretary problem in which the objective is to minimize the expected rank is seen to have a value smaller than 7/3 for all n (the number of options). This can be achieved by a simple memoryless threshold rule. The asymptotically optimal value for the class of such rules is about 2.3266. For a large finite number of options, the optimal stopping rule depends on the whole seq...

In a stochastic and fuzzy environment, two kinds of stopping models are discussed and compared. The optimal fuzzy stopping times are given under the assumptions of monotonicity and regularity for stopping rules. Also, we find that fuzzy stopping times are favored in a comparison between fuzzy and classical stopping models. Q 2000 Academic Press