Exponential Boundedness of Control Variables in a Sequentially Planned Bayesian Multiple Decision Problem in Continuous Time - Roters, Markus (Sequential analysis, 2003)
In this article we study the exponential boundedness properties of certain specifically structured control variables in a finite sequentially planned Bayesian multiple decision problem in continuous time investigated by Roters (Roters, M. A sequentially planned Bayesian multiple decision problem in continuous time. Sequential Anal. 2002, 21, 59-86.). More precisely, we prove that the total sampling time, the number of observation stages und the total sampling cost associated with these control variables possess a moment generating function in a neighborhood of the origin. All these appealing properties hold for the optimal control variable found in Roters (Roters, M. A sequentially planned Bayesian multiple decision problem in continuous time. Sequential Anal. 2002, 21, 59-86.).