Numerical Approximation for a Stochastic Fractional Differential Equation Driven by Integrated Multiplicative Noise

James Hoult and Yubin Yan ()
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James Hoult: Department of Mathematical and Physical Sciences, University of Chester, Chester CH1 4BJ, UK
Yubin Yan: Department of Mathematical and Physical Sciences, University of Chester, Chester CH1 4BJ, UK

Mathematics, 2024, vol. 12, issue 3, 1-18

Abstract: We consider a numerical approximation for stochastic fractional differential equations driven by integrated multiplicative noise. The fractional derivative is in the Caputo sense with the fractional order α ∈ ( 0 , 1 ) , and the non-linear terms satisfy the global Lipschitz conditions. We first approximate the noise with the piecewise constant function to obtain the regularized stochastic fractional differential equation. By applying Minkowski’s inequality for double integrals, we establish that the error between the exact solution and the solution of the regularized problem has an order of O ( Δ t α ) in the mean square norm, where Δ t denotes the step size. To validate our theoretical conclusions, numerical examples are presented, demonstrating the consistency of the numerical results with the established theory.

Keywords: stochastic fractional differential equations; convergence order; regularit; Brownian motion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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