Carathéodory approximate solutions for a class of stochastic differential equations involving the local time at point zero with one-sided Lipschitz continuous drift coefficients

Hiderah Kamal ()
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Hiderah Kamal: Department of Mathematics, Faculty of Science, Aden University, Aden, Yemen

Monte Carlo Methods and Applications, 2022, vol. 28, issue 2, 189-198

Abstract: In this paper, we study the Carathéodory approximate solution for a class of stochastic differential equations involving the local time at point zero. Based on the Carathéodory approximation procedure, we prove that stochastic differential equations involving the local time at point zero have a unique solution, and we show that the Carathéodory approximate solution converges to the solution of stochastic differential equations involving the local time at point zero with one-sided Lipschitz drift coefficient.

Keywords: Euler–Maruyama approximation; strong convergence; stochastic differential equations; maximum process; Carathéodory approximate solution; local time; one-sided Lipschitz condition (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1515/mcma-2022-2107

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