Martingale Representation and Logarithmic-Sobolev Inequality for Fractional Ornstein-Uhlenbeck Measure

2015/12/11 by Xiaoxia Sun, Feng Guo, Sun, Xiaoxia +1
Mathematics · #60G22 #FOS: Mathematics #Mathematical Inequalities and Applications #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Probability (math.PR) #math.PR #msc:60G22

paper · pdf · doi:10.48550/arxiv.1512.03545

14 pages

arxiv created 2015/12/11 · openalex publication_date 2015/12/11 · arxiv updated 2015/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the measure determined by a fractional Ornstein-Uhlenbeck process. For such measure, we establish a martingale representation theorem and consequently obtain the Logarithmic-Sobolev inequality. To this end, we also present the integration by parts formula for such measure, which is obtained via its pull back formula and the Bismut method.

Citations

• Logarithmic Sobolev Inequalities

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