Geodesic
Convergence rates of the Semi-Discrete method for stochastic differential equations
Teoriâ slučajnyh processov, Tome 24 (2019) no. 2, pp. 89-100

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We study the convergence rates of the semi-discrete (SD) method originally proposed in Halidias (2012), Semi-discrete approximations for stochastic differential equations and applications, International Journal of Computer Mathematics, 89(6). The SD numerical method was originally designed mainly to reproduce qualitative properties of nonlinear stochastic differential equations (SDEs). The strong convergence property of the SD method has been proved, but except for certain classes of SDEs, the order of the method was not studied. We study the order of ${\mathcal L}^2$-convergence and show that it can be arbitrarily close to $1/2.$ The theoretical findings are supported by numerical experiments.
Keywords: Explicit Numerical Scheme, Semi-Discrete Method, non-linear SDEs Stochastic Differential Equations, Boundary Preserving Numerical Algorithm. 
@article{THSP_2019_24_2_a6,
     author = {I. S. Stamatiou and N. Halidias},
     title = {Convergence rates of the {Semi-Discrete} method for stochastic differential equations},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {89--100},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2019_24_2_a6/}
}
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I. S. Stamatiou; N. Halidias. Convergence rates of the Semi-Discrete method for stochastic differential equations. Teoriâ slučajnyh processov, Tome 24 (2019) no. 2, pp. 89-100. http://geodesic.mathdoc.fr/item/THSP_2019_24_2_a6/