2009/05/06 by Jérémie Unterberger, Unterberger, Jérémie
Economics, Econometrics and Finance · #Stochastic processes and financial applications #Financial Risk and Volatility Modeling #Credit Risk and Financial Regulations
paper · doi:10.48550/arxiv.0905.0782
As a general rule, differential equations driven by a multi-dimensional irregular path Γ are solved by constructing a rough path over Γ. The domain of definition ? and also estimates ? of the solutions depend on upper bounds for the rough path; these general, deterministic estimates are too crude to apply e.g. to the solutions of stochastic differential equations with linear coefficients driven by a Gaussian process with Hölder regularity α< 1/2. We prove here (by showing convergence of Chen's series) that linear stochastic differential equations driven by analytic fractional Brownian motion [7, 8] with arbitrary Hurst index α∈ (0, 1) may be solved on the closed upper halfplane, and that the solutions have finite variance.