Journal Article10.1016/J.CHAOS.2019.04.040
Chebyshev cardinal wavelets for nonlinear stochastic differential equations driven with variable-order fractional Brownian motion
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TL;DR: In this paper, a computational approach based on the Chebyshev cardinal wavelets for a novel class of nonlinear stochastic differential equations characterized by the presence of variable-order fractional Brownian motion was proposed.
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Abstract: This paper is concerned with a computational approach based on the Chebyshev cardinal wavelets for a novel class of nonlinear stochastic differential equations characterized by the presence of variable-order fractional Brownian motion. More precisely, in the proposed approach, the solution of a nonlinear stochastic differential equation is approximated by the Chebyshev cardinal wavelets and subsequently the intended problem is transformed to a system of nonlinear algebraic equations. In this way, the nonlinear terms are significantly reduced, due to the cardinal property of the basis functions used. The convergence analysis of the expressed method is theoretically investigated. Moreover, the reliability and applicability of the approach are experimentally examined through the numerical examples. In addition, the presented method is implemented for some famous stochastic models, such as stochastic logistic problem, stochastic population growth model, stochastic Lotka–Volterra problem, stochastic Brusselator problem, stochastic Duffing-Van der Pol oscillator problem and stochastic pendulum model. As another new finding, a procedure is established for constructing the variable-order fractional Brownian motion. Indeed, the standard Brownian motion together with the block pulse functions and the hat functions are utilized for generating the variable-order fractional Brownian motion.
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References
•Book
Numerical Solution of Stochastic Differential Equations
Peter E. Kloeden,Eckhard Platen +1 more
- 01 Jun 1992
TL;DR: In this article, a time-discrete approximation of deterministic Differential Equations is proposed for the stochastic calculus, based on Strong Taylor Expansions and Strong Taylor Approximations.
6.5K
The variation of certain speculative prices
TL;DR: The classic model of the temporal variation of speculative prices (Bachelier 1900) assumes that successive changes of a price Z(t) are independent Gaussian random variables as discussed by the authors.
5K
•Book
Spectral Methods in Fluid Dynamics
M. Y. Hussaini,Thomas A. Zang +1 more
- 01 Jan 1987
TL;DR: Spectral methods have been widely used in simulation of stability, transition, and turbulence as discussed by the authors, and their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed.
5K
•Posted Content
The Variation of Certain Speculative Prices
TL;DR: In this article, a new model of price behavior in speculative markets is proposed, which is a generalization of the continuous random walk of Bachelier process applied to InZ(t) instead of Z(t), where the Gaussian distribution is replaced throughout by another family of probability laws referred to as stable Paretian.
4.1K
Spectral Methods in Fluid Dynamics.
TL;DR: In this article, the authors present a set of methods for the estimation of two-dimensional fluid flow, including a Fourier Galerkin method and a Chebyshev Collocation method.
3.7K