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A note on the Euler–Maruyama scheme for 1-dimensional stochastic differential equations involving the local time of the unknown process.
- Source :
-
Journal of Interdisciplinary Mathematics . Dec 2021, Vol. 24 Issue 8, p2215-2235. 21p. - Publication Year :
- 2021
-
Abstract
- In this paper, we study both strong and weak rate of convergence of Euler-Maruyama scheme for one-dimensional stochastic differential equations involving the local time (SDELT) of the unknown process, whose the solution corresponds to divergence form operator with a discontinuous coefficients at point ξ ∈ ℝ. The paper is concerned with stochastic differential equation with local time of type, where is the local time of X in {ξ}. The main idea of this paper is to use a space transform in order to transform the original SDELT to a new auxiliary equation with discontinuous coefficients but without local time. Then, we apply the Euler-Maruyama scheme to this new equation. Finally, we obtain an approximation of the original SDELT by transforming the approximation of the auxiliary equation. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DISCONTINUOUS coefficients
Subjects
Details
- Language :
- English
- ISSN :
- 09720502
- Volume :
- 24
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Journal of Interdisciplinary Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 154689971
- Full Text :
- https://doi.org/10.1080/09720502.2021.1893474