Cameron--Martin Type Theorem for a Class of non-Gaussian Measures

2023/12/25 by Mohamed Erraoui, Michael Röckner, Erraoui, Mohamed +3
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #28C20 #46G10 #60G22 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Probability (math.PR) #Statistical Mechanics and Entropy #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2312.15695

openalex publication_date 2023/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the quasi-invariant property of a class of non-Gaussian measures. These measures are associated with the family of generalized grey Brownian motions. We identify the Cameron--Martin space and derive the explicit Radon-Nikodym density in terms of the Wiener integral with respect to the fractional Brownian motion. Moreover, we show an integration by parts formula for the derivative operator in the directions of the Cameron--Martin space. As a consequence, we derive the closability of both the derivative and the corresponding gradient operators.

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