Approximations for adapted M-solutions of type-II backward stochastic Volterra integral equations
抄録
<jats:p>In this paper, we study a class of Type-II backward stochastic Volterra integral equations (BSVIEs). For the adapted M-solutions, we obtain two approximation results, namely, a BSDE approximation and a numerical approximation. The BSDE approximation means that the solution of a finite system of backward stochastic differential equations (BSDEs) converges to the adapted M-solution of the original equation. As a consequence of the BSDE approximation, we obtain an estimate for the <jats:italic>L</jats:italic><jats:sup>2</jats:sup>-time regularity of the adapted M-solutions of Type-II BSVIEs. For the numerical approximation, we provide a backward Euler-Maruyama scheme, and show that the scheme converges in the strong <jats:italic>L</jats:italic><jats:sup>2</jats:sup>-sense with the convergence speed of order 1/2. These results hold true without any differentiability conditions for the coefficients.</jats:p>
収録刊行物
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- ESAIM: Probability and Statistics
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ESAIM: Probability and Statistics 27 19-79, 2023
EDP Sciences