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In this paper, we formulate the cooperative transmission problem as multiple stopping problem in CRNs.
We, then, formulate our cooperative relay selection problem as an optimal multiple stopping problem in the sum case.
After deriving the reward function, we summarize the optimal multiple stopping problem in cooperative relay selection as follows: the PU pair receives the reward Y k after the kth observations, then the PU transmitter makes a decision on whether to make a stop at the current candidate relay.
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In this subsection, we solve the multiple stopping problems in the sum case by deriving the optimality equations.
The VIs, and consequently the present multiple optimal stopping problem, turn out to be exactly solvable.
This paper focused on a solvable multiple optimal stopping problem related to animal migration.
The present multiple optimal stopping problem is a simple theoretical model for migration of animals, migratory fishes in particular [16].
We are interested in solvability of a multiple optimal stopping problem that has not been focused on so far, which is related to animal migration: an important ecological problem.
The recursive equations (6) and (7) are later utilized to show that the present multiple optimal stopping problem results in a cascading system of VIs that can be solved in a cascading manner from (i = M) to (i = 1).
We consider a multiple optimal stopping problem of finding the collection of the stopping times (tau = ( tau_{1},ldots2},tau_{,tau_{M} )) ((0 = tau_{0} le tau_{1} le tau_{2}lecdots le tau_{M}), (M ge 1) is a given natural number) with no refraction.
Multiple optimal stopping problems based on stochastic differential equations (SDEs) are among the ones that have been analyzed most in detail because of their rich mathematical structures [8, 9].
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