Integral with respect to the G-Brownian local time

2012/12/27 by Litan Yan, Yan, Litan, Xichao Sun +3
Economics, Econometrics and Finance · Mathematics · #60G05 #60G20 #60H05 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Probability (math.PR) #Stochastic processes and financial applications #math.FA #math.PR #msc:60G05 #msc:60G20 #msc:60H05

paper · pdf · doi:10.48550/arxiv.1212.6353

24 pages

arxiv created 2012/12/27 · openalex publication_date 2012/12/27 · arxiv updated 2013/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathscr L be the local time of G-Brownian motion B. In this paper, we prove the existence of the quadratic covariation <f(B),B>_t and the integral ∫_{\mathbb R}f(x)\mathscr L(dx,t). Moreover, a sublinear version of the Bouleau-Yor identity ∫_{\mathbb R}f(x)\mathscr L(dx,t)=-<f(B),B>_t is showed to hold under some suitable conditions. These allow us to write the Itô's formula for C¹-functions.

Citations

• G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty

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