|
|||||
|
|
A note on the gambling team method |
|
| Institution: | 1. State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum Beijing (CUP), Beijing, 102249, China;2. University of Texas at Austin, Austin, 78731, Texas, USA;1. School of Oceanographic studies, Jadavpur University, 188 Raja SCM Road, Kolkata 700032, India;2. Geological Survey of India, CHQ, Kolkata, India;3. Indian Institute of Remote Sensing, Dehradun, India;1. Department of Mathematical Sciences, University of Illinois, United States;2. Bolyai Institute, University of Szeged, Hungary;3. Department of Mathematics, Iowa State University, Ames, IA 50011, United States;4. Department of Computer Science, University of Szeged, Hungary |
| Abstract: | Gerber and Li (1981) formulated, using a Markov chain embedding, a system of equations that describes relations between generating functions of waiting time distributions for occurrences of patterns in a sequence of independent repeated experiments when the initial outcomes of the process are known. We show how this system of equations can be obtained by using the classical gambling team technique. We also present a form of solution of the system and give an example showing how first results of trials influence the probabilities that a chosen pattern precedes the remaining ones in a realization of the process. |
| Keywords: | Martingales Stopping times Optional stopping theorem Gambling team technique Generating functions |
| 本文献已被 ScienceDirect 等数据库收录！ | |