Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)
Improved local approximation for multidimensional diffusions: the G-rates
S. Bodnarchuk, D. Ivanenko, A. Kohatsu-Higa, A. Kulik
Abstract: In this article, we consider the problem of improving the local approximations for multidimensional diffusions. In particular, our proposed explicit approximation improves the Milshtein approximation. We also provide a semi-explicit convergence rate estimate (we call it G-rate) for the proposed local approximation. The main error term in the difference of densities is bounded by a polynomial multiplied by a Gaussian density and the remainder is exponentially small as time goes to zero.
Keywords: Expansions, Stochastic Differential Equations, Total Variation Distance
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