V. D. L. Peña

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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 $P (T_{b} < \infty) \leq 1/ b$ …

math.PR2025

Decoupling for Markov Chains

Nawaf Bou-Rabee, Victor H. de la PeÃ±a

Consider a Markov chain $(X_{i})_{i \geq 0}$ with invariant measure $I^¼$ that admits the representation $X_{i + 1} = I^¦ (X_{i}, U_{i})$ , where $(U_{i})_{i \geq 0}$ are i.i.d. random variables and $I^¦$ …

math.PR2025

Sharp Decoupling Inequalities for the Variances and Second Moments of Sums of Dependent Random Variables

Victor H. de la Pena, Heyuan Yao, Demissie Alemayehu

Both complete decoupling and tangent decoupling are classical tools aiming to compare two random processes where one has a weaker dependence structure. We give a new proof for the…