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Numerical Implementation of Stochastic Operational Matrix Driven by a Fractional Brownian Motion for Solving a Stochastic Differential Equation

Author

Listed:
  • R. Ezzati
  • M. Khodabin
  • Z. Sadati

Abstract

An efficient method to determine a numerical solution of a stochastic differential equation (SDE) driven by fractional Brownian motion (FBM) with Hurst parameter H ∈ (1/2, 1) and n independent one‐dimensional standard Brownian motion (SBM) is proposed. The method is stated via a stochastic operational matrix based on the block pulse functions (BPFs). With using this approach, the SDE is reduced to a stochastic linear system of m equations and m unknowns. Then, the error analysis is demonstrated by some theorems and defnitions. Finally, the numerical examples demonstrate applicability and accuracy of this method.

Suggested Citation

  • R. Ezzati & M. Khodabin & Z. Sadati, 2014. "Numerical Implementation of Stochastic Operational Matrix Driven by a Fractional Brownian Motion for Solving a Stochastic Differential Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:523163
    DOI: 10.1155/2014/523163
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    References listed on IDEAS

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    1. Pei Cheng & Fengqi Yao & Mingang Hua, 2014. "Stability Analysis of Impulsive Stochastic Functional Differential Equations with Delayed Impulses via Comparison Principle and Impulsive Delay Differential Inequality," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, February.
    2. Wenhua Gao & Feiqi Deng & Ruiqiu Zhang & Wenhui Liu, 2014. "Finite‐Time H∞ Control for Time‐Delayed Stochastic Systems with Markovian Switching," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Wenhua Gao & Feiqi Deng & Ruiqiu Zhang & Wenhui Liu, 2014. "Finite-Time Control for Time-Delayed Stochastic Systems with Markovian Switching," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, February.
    4. Pei Cheng & Fengqi Yao & Mingang Hua, 2014. "Stability Analysis of Impulsive Stochastic Functional Differential Equations with Delayed Impulses via Comparison Principle and Impulsive Delay Differential Inequality," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Longjin, Lv & Ren, Fu-Yao & Qiu, Wei-Yuan, 2010. "The application of fractional derivatives in stochastic models driven by fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4809-4818.
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