Stability of the split-step backward Euler scheme for stochastic delay integro-differential equations with Markovian switching |
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| Institution: | 1. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;2. College of Computer Science, South Central University for Nationalities, Wuhan 430074, China;1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China;2. School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041000, Shanxi Province, China;3. Center for Applied Mathematics, Tianjin University, Tianjin 300072, China;1. School of Mathematics and Statistics & Research Institute of Mathematical Science, Jiangsu Normal University, Xuzhou, Jiangsu 221000, PR China;2. School of Mathematics, Shandong University, Jinan, Shandong 250100, PR China;1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China;2. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, United States of America;3. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China;1. Department of Biomedical Engineering, Boston University, 44 Cummington Street, Boston, MA 02215, USA;2. Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA;3. Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK;4. Centre de Recerca Matematica, Campus de Bellaterra, Edifici C, 08193 Bellaterra (Barcelona), Spain;5. Departament de Matemàtiques, Universitat Atonòma de Barcelona, 08193 Bellaterra (Barcelona), Spain;6. Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK;7. Computational Biology Group, Department of Computer Science, University of Oxford, Oxford OX1 3QD, UK |
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| Abstract: | In this paper, we concentrate on the numerical approximation of solutions of stochastic delay integro-differential equations with Markovian switching (SDIDEsMS). We establish the split-step backward Euler (SSBE) scheme for solving linear SDIDEsMS and discuss its convergence and stability. Moreover, the SSBE method is convergent with strong order γ = 1/2 in the mean-square sense. The conditions under which the SSBE method is mean-square stable and general mean-square stable are obtained. Some illustrative numerical examples are presented to demonstrate the stability of the numerical method and show that SSBE method is superior to Euler method. |
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