Large Deviation Theory

Abstract

This chapter applies Wentzell’s theory of large deviation s to the Wright–Fisher model, using the approach of Papangelou (Athens conference on applied probability and time series analysis. Lecture notes in statistics, vol 114. Springer, New York, pp 245–252, 1996; Papangelou, Ann Appl Probab, 8(1):182–192, 1998; Papangelou, Stochastic processes and related topics. Trends in mathematics. Birkhäuser, Boston, pp 315–330, 1998; Papangelou, Ann Appl Probab 10(4):1259–1273, 2000). For a different approach to the large deviation principle for exit times in population genetics, we refer the reader to Morrow and Sawyer (Ann Probab 17(3):1124–1146, 1989) and Morrow (Ann Appl Probab 2(4):857–905, 1992). As customary, we shall abbreviate Large Deviation Principle as LDP.