In recent publication, Professor Emerita Alexandria Rodkina (Department of Mathematics, Faculty of Science and Technology, The UWI Mona) and collaborator considered a stochastic dynamical system in the form of difference equation which was perturbed by a sequence of independent random variables. They have developed necessary and sufficient conditions of asymptotic stability of the solution of this equation. For the proof they applied Kolmogorov's variant of the strong law of large numbers as well as martingale convergence and martingale representation theorems. The system under consideration can be used for modeling in mathematical finance and mathematical biology.
Reference: A. Rodkina, H. Shurz, A Martingale Approach to Asymptotic Stability of Nonlinear Stochastic Difference Equations With Bounded Noise in R1, Dynamic Systems and Applications 32(1), 2023. DOI: 10.46719/dsa2023.32.08
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Published on 26 Mar, 2024
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