Limit distributions for the discretization error of stochastic Volterra equations

2021/12/13 by Fukasawa, Masaaki, Ugai, Takuto
#FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2112.06471

Abstract

Our study aims to specify the asymptotic error distribution in the discretization of a stochastic Volterra equation with a fractional kernel. It is well-known that for a standard stochastic differential equation, the discretization error, normalized with its rate of convergence 1/√(n), converges in law to the solution of a certain linear equation. Similarly to this, we show that a suitably normalized discretization error of the Volterra equation converges in law to the solution of a certain linear Volterra equation with the same fractional kernel.

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