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Exit times in non-Markovian drifting continuous-time random walk processes
non-Markovian drifting continuous-time random walk processes
2010/10/18
By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it d...
A general "bang-bang" principle for predicting the maximum of a random walk
Bernoulli random walk Brownian motion optimal prediction ultimate maximum stopping time convex function
2010/11/2
Let (Bt)0tT be either a Bernoulli random walk or a Brownian motion with drift, and let Mt := max{Bs : 0 s t}, 0 t T. This paper solves the general optimal prediction problem sup 0 T E[f(MT...