A few comments on a result of A. Novikov and Girsanov's theorem. Issue 8 (17th November 2019)

• Record Type: Journal Article
• Authors: Krylov, N. V.
• Is Part Of: Stochastics. Volume 91:Issue 8(2019)
• Page Start: 1186
• Page End: 1189
• Publication Date: 2019-11-17
• Subjects: Exponential martingales -- Novikov's condition -- Girsanov's theorem; 60G44 -- 60H10; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2019.1590356
• Languages: English
• ISSNs: 1744-2508

Abstract

ABSTRACT: We give a simple proof that for a continuous local martingale M t lim _ ε ↓ 0 ⁡ ε log ⁡ E e ( 1 − ε ) ⟨ M ⟩ ∞ / 2 < ∞ ⟹ E exp ⁡ ( M ∞ − ⟨ M ⟩ ∞ / 2 ) = 1.