Stopping for N-Parameter Stochastic Processes
Wang Sheng-xi
Abstract
Wang Sheng-xi
Abstract
In this paper,the past of a stopping point is defined.The infimum of two stopping points is obtained and the stopping for N-Parameter martingale is defined.It proves that every stoped N-Parameter S-martingale at a stopping point is still a S-martingale if the filtrations {F\-t} sttisfies the condition \$g(F\-4)\$ and they are equivalent to the stranger Doob stopping theorem.
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In this paper,the past of a stopping point is defined.The infimum of two stopping points is obtained and the stopping for N-Parameter martingale is defined.It proves that every stoped N-Parameter S-martingale at a stopping point is still a S-martingale if the filtrations {F\-t} sttisfies the condition \$g(F\-4)\$ and they are equivalent to the stranger Doob stopping theorem.
Key concepts: Infimum and supremum, Optional stopping theorem, Martingale (probability theory), Stopping time, Mathematics, Optimal stopping, Local martingale, Doob's martingale inequality