Weak approximation of a fractional SDE

2007/09/06 by Xavier Bardina, Ivan Nourdin, Bardina, Xavier +5
Economics, Econometrics and Finance · Mathematics · #60H05 #60H10 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60H05 #msc:60H10

paper · pdf · doi:10.48550/arxiv.0709.0805

32 pages; this is a major revision, with two additional co-authors (X. Bardina and C. Rovira)

openalex publication_date 2007/09/06 · arxiv created 2008/12/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, a diffusion approximation result is shown for stochastic differential equations driven by a (Liouville) fractional Brownian motion B with Hurst parameter H in (1/3,1/2). More precisely, we resort to the Kac-Stroock type approximation using a Poisson process studied in Bardina, Jolis and Tudor (2003) and Delgado and Jolis (2000), and our method of proof relies on the algebraic integration theory introduced by Gubinelli (2004).

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