A note on weak existence for SDEs driven by fractional Brownian motion

2023/03/31 by Lukas Anzeletti, Anzeletti, Lukas
Economics, Econometrics and Finance · Mathematics · #34A06 #60G22 #60H10 #60H50 #Economic theories and models #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2303.17970

openalex publication_date 2023/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We are interested in existence of solutions to the d-dimensional equation X_t=x₀+∫₀^t b(X_s)ds + B_t, where B is a (fractional) Brownian motion with Hurst parameter H\leqslant 1/2 and b is an ℝ^d-valued measure in some Besov space. We exhibit a class of drifts b such that weak existence holds. In particular existence of a weak solution is shown for b being a finite ℝ^d-valued measure for any H<1/(2d).

Related

• Weak approximation of fractional SDES: The Donsker setting
• Weak existence for SDEs with singular drifts and fractional Brownian or Levy noise beyond the subcritical regime
• Weak convergence of path-dependent SDEs driven by fractional Brownian motion with irregular coefficients
• Strong solutions of SDE's with generalized drift and multidimensional\n fractional Brownian initial noise
• Weak existence of a solution to a differential equation driven by a very rough fBm