A simple proof of a result of A. Novikov

2002/07/01 by Н. В. Крылов, Nicolai Krylov, Krylov, Nicolai · 1 citation
Computer Science · Mathematics · #60H05 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Spectral Theory in Mathematical Physics #math.PR #msc:60H05

paper · pdf · doi:10.48550/arxiv.math/0207013

3 pages, few glitches corrected

openalex publication_date 2002/07/01 · arxiv created 2009/05/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give simple proofs that for a continuous local martingale M_t: 1) \liminf_ε->0 εlog Ee^{(1-ε) <M>_∞ /2} < ∞ ==> Eexp(M_∞ - <M>_∞ /2) = 1, 2) \liminf_ε->0 εlogsup_t>=0 Ee^(1-ε)M_t/2 < ∞ ==> Eexp(M_∞ - <M>_∞ /2) = 1 .

Cited by

• From CKLS Process to CIR-type and OU-type Processes: Using a Twice-differentiable Mapping and Generalized Girsanov's Theorem

Related

• On the Martingale Property of Certain Local Martingales
• When a Stochastic Exponential is a True Martingale. Extension of a Method of Bene^s
• On local martingale and its supremum: harmonic functions and beyond
• Strict Local Martingales via Filtration Enlargement
• A Weak Convergence Criterion Constructing Changes of Measure