M. Klass

collaborators

2 papers

math.PR2026

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 ${M_{n}}$ and any extended-valued s…

math.PR2026

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 $(M_{n})$ with $M_{0} = 1$ , let $T_{b}$ be the first time it reaches a level $b > 1$ . Ville's inequality gives only the bound $P (T_{b} < \infty) \leq 1/ b$ …