2010/10/19 by Wenbo V. Li, Li, Wenbo V., Vladislav Vysotsky +2
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60G50 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics #math.PR #msc:60G50
paper · pdf · doi:10.48550/arxiv.1010.4063
11 figures
openalex publication_date 2010/10/19 · arxiv created 2012/03/16 · arxiv updated 2012/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Suppose you and your friend both do n tosses of an unfair coin with probability of heads equal to α. What is the behavior of the probability that you obtain at least d more heads than your friend if you make r additional tosses? We obtain asymptotic and monotonicity/convexity properties for this competing probability as a function of n, and demonstrate surprising phase transition phenomenons as parameters d, r and α vary. Our main tools are integral representations based on Fourier analysis.