Numerical solution and simulation of random differential equations with Wiener and compound Poisson Processes

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MOMENI A.; Kamrani m.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2019 | Volume:5 | Issue:19 Page(s): 93-106

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Title

Numerical solution and simulation of random differential equations with Wiener and compound Poisson Processes

Author(s)

MOMENI A. | Kamrani m. | Issue Writer Certificate

Keywords

Random differential equationsQ1

Random affine equationsQ1

Order of convergenceQ1

Stochastic Taylor methodQ1

Compound poisson processesQ1

Abstract

Ordinary differential equations(ODEs) with stochastic processes in their vector field, have lots of applications in science and engineering. The main purpose of this article is to investigate the numerical methods for ODEs with Wiener and Compound poisson processes in more than one dimension. Ordinary differential equations with Ito diffusion which is a solution of an Ito stochastic differential equation will be considered. Because for the numerical solution of these equations we need the simulation of stochastic double integrals, we explain the simulation of these integrals in more details. Also one-step and multi steps methods for the solution of affine random ordinary equations (RODEs) which are an important class of RODEs will be considered. The numerical solution of these equations with Wiener and Compound poisson processes will be established. Two methods for simulation of the double integrals will be explained, and some numerical examples are provided to confirm the theoretical results numerically.

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APA: Copy

MOMENI, A., & Kamrani, m.. (2019). Numerical solution and simulation of random differential equations with Wiener and compound Poisson Processes. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 5(19 ), 93-106. SID. https://sid.ir/paper/257342/en

Vancouver: Copy

MOMENI A., Kamrani m.. Numerical solution and simulation of random differential equations with Wiener and compound Poisson Processes. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2019;5(19 ):93-106. Available from: https://sid.ir/paper/257342/en

IEEE: Copy

A. MOMENI, and m. Kamrani, “Numerical solution and simulation of random differential equations with Wiener and compound Poisson Processes,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 5, no. 19 , pp. 93–106, 2019, [Online]. Available: https://sid.ir/paper/257342/en

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