NUMERICAL SOLUTION OF PERSISTENT PROCESSES-BASED FRACTIONAL STOCHASTIC DIFFERENTIAL EQUATIONS

D. Uma, S. Raja Balachandar, S. G. Venkatesh, K. Balasubramanian and Mantepu Tshepo Masetshaba
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D. Uma: Department of Mathematics, School of Arts, Sciences and Humanities, SASTRA Deemed University, Thanjavur 613401, Tamilnadu, India
S. Raja Balachandar: Department of Mathematics, School of Arts, Sciences and Humanities, SASTRA Deemed University, Thanjavur 613401, Tamilnadu, India
S. G. Venkatesh: Department of Mathematics, School of Arts, Sciences and Humanities, SASTRA Deemed University, Thanjavur 613401, Tamilnadu, India
K. Balasubramanian: ��Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed University, Kumbakonam 612001, Tamil Nadu, India
Mantepu Tshepo Masetshaba: ��Department of Decision Sciences, University of South Africa, UNISA 0003, South Africa

FRACTALS (fractals), 2023, vol. 31, issue 04, 1-14

Abstract: This paper proposes the shifted Legendre polynomial approximations-based stochastic operational matrix of integration method to solve persistent processes-based fractional stochastic differential equations. The operational matrix of integration, stochastic operation matrix and fractional stochastic operational matrix of the shifted Legendre polynomials are derived. The stochastic differential equation is transformed into an algebraic system of (N + 1) equations by the operational matrices. For the proposed approach, a thorough discussion of the error analysis in L2 norm is provided. The proposed method’s applicability, correctness, and accuracy are examined using a few numerical examples. Comparing the numerical examples to the other methods discussed in the literature demonstrates the solution’s effectiveness and attests to the solution’s high quality. The error analysis also reveals the method’s superiority. A more accurate solution is obtained, thus maintaining a minimum error.

Keywords: Stochastic Differential Equations; Stochastic Operational Matrix; Shifted Legendre Polynomial; Fractional Brownian Motion; Hurst Parameter; Persistent Process; Error Analysis (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400522

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