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Improved rectangular method on stochastic Volterra equations. (English) Zbl 1221.65023

The authors present an improved version of their rectangular method for approximating the solution of the Itô stochastic Volterra integral equation \[ X_t= x+\int^t_0 a(t, X_s)\,ds+ \int^t_0 b(t, X_s)\,dW_s, \] where \(W_t\) is a standard Brownian motion. It is proved that the approximate solutions converge with order \(h\) to the exact solution. Then a modification of the method to facilitate greater ease of computation is introduced and shown to retain the order \(h\) convergence. Numerical results for a simple example are discussed.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
37M99 Approximation methods and numerical treatment of dynamical systems
60H20 Stochastic integral equations
65C20 Probabilistic models, generic numerical methods in probability and statistics
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
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References:

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