The notion ofmartingale has proven to be among the most powerful ideas to emerge in probability in the past century.

1. 1.

   See Theorem 5.12 of S. Ramasubramanian (2009) for the asymptotic equality in the case of the Cramér-Lundberg model.

2. 2.

   A more comprehensive treatment of this class of problems is given in ChapterVIII.

3. 3.

   Historically this is the problem that lead Hugo Steinhaus to develop an axiomatic theory of repeated coin tossing based on his reading of Lebesgue’s newly developed integral and measure on the real number line. The problem is revisited in ChapterVIII.

Authors and Affiliations

1. Department of Mathematics, University of Arizona, Tucson, AZ, USA

   Rabi Bhattacharya

2. Department of Mathematics, Oregon State Univeristy, Corvallis, OR, USA

   Edward C. Waymire

Corresponding author

Correspondence toRabi Bhattacharya.

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