Wasserstein approximations of the Lévy area random walk via polynomial perturbations of Gaussian distributions

2016/05/29 by Guy Flint, Flint, Guy
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Geometric Analysis and Curvature Flows #Probability (math.PR) #Stochastic processes and financial applications #math.PR

paper · pdf · doi:10.48550/arxiv.1605.08996

arxiv created 2016/05/29 · openalex publication_date 2016/05/29 · arxiv updated 2016/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a coupling between the random walk composed of Lévy area increments from a d-dimensional Brownian motion and a random walk composed of quadratic polynomials of Gaussian random variables. This coupling construction is used to produce a new pathwise approximation scheme for stochastic differential equations in the preprint [Flint-Lyons-2015]. The coupling arguments of the present paper are based extensively on the recent coupling results of Davie concerning a multidimensional variant of the Komlós-Major-Tusnády theorem and Wasserstein estimates for polynomial perturbations of Gaussian measures.

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