An Algebraic Approach to the Cameron-Martin-Maruyama-Girsanov Formula
Jiro Akahori, Takafumi Amaba, Sachiyo Uraguchi
TL;DR
This paper presents a novel algebraic proof of the Cameron-Martin-Maruyama-Girsanov formula, utilizing exponentiation of Malliavin-type differentiation and its adjointness to provide a new perspective.
Contribution
It introduces an entirely algebraic approach to prove the Cameron-Martin-Maruyama-Girsanov formula, differing from traditional analytical proofs.
Findings
Provides an algebraic proof of the formula
Highlights the role of Malliavin calculus in stochastic analysis
Offers new insights into the structure of measure transformations in stochastic processes
Abstract
In this paper, we will give a new perspective to the Cameron-Martin-Maruyama-Girsanov formula by giving a totally algebraic proof to it. It is based on the exponentiation of the Malliavin-type differentiation and its adjointness.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Nonlinear Waves and Solitons · Advanced Differential Equations and Dynamical Systems