46 citations · 64 across the 4 of their papers we have counts for
4 papers
The Exact Ville Identity: From the Absorbing Case to the General Law with an Application to E-Values
Victor H. de la Pena, Michael J. Klass
For a nonnegative supermartingale with , let be the first time it reaches a level . Ville's inequality gives only the bound …
Beyond Wald's Equation and the Optional Sampling Theorem
Michael J. Klass, Victor H. de la Pena
This paper establishes a conservation identity for mean-zero martingales stopped by extended-valued stopping times. For any mean-zero martingale and any extended-valued s…
Pseudo-maximization and self-normalized processes
Victor H. de la Peña, Michael J. Klass, Tze Leung Lai
Self-normalized processes are basic to many probabilistic and statistical studies. They arise naturally in the the study of stochastic integrals, martingale inequalities and limit…
Self-normalized processes: exponential inequalities, moment bounds and iterated logarithm laws
Victor H. de la Pena, Michael J. Klass, Tze Leung Lai
Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or wea…