Lie symmetry analysis, conservation laws and numerical approximations of time-fractional Fokker–Planck equations for special stochastic process in foreign exchange markets

Noora Habibi, Elham Lashkarian, Elham Dastranj and S. Reza Hejazi

Physica A: Statistical Mechanics and its Applications, 2019, vol. 513, issue C, 750-766

Abstract: In this paper the transition joint probability density function of the solution of the Ornstein–Uhlenbeck process is presented by a deterministic parabolic time-fractional PDE (FPDE), named time-fractional Fokker–Planck equation. The article generally is divided to two parts: theoretical and approximated analysis. In the theoretical sections Lie group method and invariant subspace method are applied for finding exact solutions and conservation laws of the considered equation. In the next part, by Chebyshev wavelets’s method the numerical solutions are driven. Then the usefulness of this approximated method is comparing with the exact solutions by some plotted graphs.

Keywords: Fokker–Planck equation; Ornstein–Uhlenbeck process; Lie symmetry; Invariant subspace method; Chebyshev wavelets’s polynomial (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:513:y:2019:i:c:p:750-766

DOI: 10.1016/j.physa.2018.08.155

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