Interval neutrosophic stochastic dynamical systems driven by Brownian motion

• Published in: Applied soft computing 2022-11, Vol.129, p.109609, Article 109609
• Main Authors: Son, Nguyen Thi Kim, Dong, Nguyen Phuong, Long, Hoang Viet, Kumar, Raghvendra, Priyadarshini, Ishaani
• Format: Article
• Language: English
• Subjects: Euler–Maruyama method; Interval neutrosophic calculus; Interval neutrosophic numbers; Interval neutrosophic stochastic process
• ISSN: 1568-4946; 1872-9681
• DOI: 10.1016/j.asoc.2022.109609

Stochastic and neutrosophic theory are effective tools for modeling real-world phenomena and natural dynamical systems, where inputs are often affected by stochastic noises and outputs often contain both randomness and indeterminacy. In this work, we present a new type of stochastic differential equations (SDE) driven by an one-dimensional Brownian motion that can be considered as an efficient tool to describe the uncertain behavior of dynamical systems operating in interval neutrosophic environments with stochastic noises. After introducing some basic foundations on neutrosophic arithmetic, neutrosophic calculus and neutrosophic stochastic process, we define the new form of interval neutrosophic stochastic differential equations taking values in neutrosophic environment. Under some suitable conditions, the unique existence result of stochastic solution is obtained based on the use of Picard successive approximation. We also introduce an efficient numerical algorithm, namely Euler–Maruyama method, to solve the numerical solution of proposed problem and further demonstrate the effectiveness of the numerical method by solving some examples in stochastic biological systems such as stochastic logistic growth model, stochastic Lotka–Volterra predator–prey model, and stochastic SARS model, respectively. •Parametric representation of interval neutrosophic numbers.•Interval neutrosophic stochastic (INS) dynamic systems driven by Brownian motion.•Euler–Maruyama method for numerical INS solution.•INS biological systems such as Lotka–Volterra predator–prey and stochastic SARS model.