Chebyshev cardinal wavelets for nonlinear stochastic differential equations driven with variable-order fractional Brownian motion
Author
Abstract
Suggested Citation
DOI: 10.1016/j.chaos.2019.04.040
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- Robert J. Elliott & John Van Der Hoek, 2003. "A General Fractional White Noise Theory And Applications To Finance," Mathematical Finance, Wiley Blackwell, vol. 13(2), pages 301-330, April.
- M. H. Heydari & M. R. Hooshmandasl & F. M. Maalek Ghaini & Ming Li, 2013. "Chebyshev Wavelets Method for Solution of Nonlinear Fractional Integrodifferential Equations in a Large Interval," Advances in Mathematical Physics, Hindawi, vol. 2013, pages 1-12, October.
- Sun, HongGuang & Chen, Wen & Chen, YangQuan, 2009. "Variable-order fractional differential operators in anomalous diffusion modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4586-4592.
- Benoit Mandelbrot, 2015.
"The Variation of Certain Speculative Prices,"
World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78,
World Scientific Publishing Co. Pte. Ltd..
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394-394.
- Heydari, M.H. & Hooshmandasl, M.R. & Maalek Ghaini, F.M. & Cattani, C., 2016. "Wavelets method for solving fractional optimal control problems," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 139-154.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- P. K. Singh & S. Saha Ray, 2024. "A Collocation Method for Nonlinear Stochastic Differential Equations Driven by Fractional Brownian Motion and its Application to Mathematical Finance," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-23, June.
- Mirzaee, Farshid & Solhi, Erfan & Naserifar, Shiva, 2021. "Approximate solution of stochastic Volterra integro-differential equations by using moving least squares scheme and spectral collocation method," Applied Mathematics and Computation, Elsevier, vol. 410(C).
- Rahimkhani, P. & Ordokhani, Y., 2022. "Chelyshkov least squares support vector regression for nonlinear stochastic differential equations by variable fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
- Mahmoudi, Mohammad Reza & Baleanu, Dumitru & Mansor, Zulkefli & Tuan, Bui Anh & Pho, Kim-Hung, 2020. "Fuzzy clustering method to compare the spread rate of Covid-19 in the high risks countries," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
- Eftekhari, Tahereh & Rashidinia, Jalil, 2022. "A novel and efficient operational matrix for solving nonlinear stochastic differential equations driven by multi-fractional Gaussian noise," Applied Mathematics and Computation, Elsevier, vol. 429(C).
- Heydari, M.H., 2020. "Chebyshev cardinal functions for a new class of nonlinear optimal control problems generated by Atangana–Baleanu–Caputo variable-order fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
- Mahmoudi, Mohammad Reza, 2021. "A computational technique to classify several fractional Brownian motion processes," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Karuppiah, Jeyanthi & Los, Cornelis A., 2005.
"Wavelet multiresolution analysis of high-frequency Asian FX rates, Summer 1997,"
International Review of Financial Analysis, Elsevier, vol. 14(2), pages 211-246.
- Cornelis A. Los & Jeyanthi Karuppiah, 2004. "Wavelet Multiresolution Analysis of High-Frequency Asian FX Rates, Summer 1997," Finance 0409037, University Library of Munich, Germany.
- Heydari, Mohammad Hossein & Avazzadeh, Zakieh, 2018. "Legendre wavelets optimization method for variable-order fractional Poisson equation," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 180-190.
- Heydari, Mohammad Hossein & Avazzadeh, Zakieh & Haromi, Malih Farzi, 2019. "A wavelet approach for solving multi-term variable-order time fractional diffusion-wave equation," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 215-228.
- Erhan Bayraktar & H. Vincent Poor & K. Ronnie Sircar, 2004.
"Estimating The Fractal Dimension Of The S&P 500 Index Using Wavelet Analysis,"
International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(05), pages 615-643.
- Erhan Bayraktar & H. Vincent Poor & Ronnie Sircar, 2007. "Estimating the Fractal Dimension of the S&P 500 Index using Wavelet Analysis," Papers math/0703834, arXiv.org.
- Eftekhari, Tahereh & Rashidinia, Jalil, 2022. "A novel and efficient operational matrix for solving nonlinear stochastic differential equations driven by multi-fractional Gaussian noise," Applied Mathematics and Computation, Elsevier, vol. 429(C).
- Stoyan V. Stoyanov & Yong Shin Kim & Svetlozar T. Rachev & Frank J. Fabozzi, 2017. "Option pricing for Informed Traders," Papers 1711.09445, arXiv.org.
- Jean-Philippe Aguilar & Jan Korbel & Yuri Luchko, 2019. "Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations," Mathematics, MDPI, vol. 7(9), pages 1-23, September.
- Paul Ormerod, 2010. "La crisis actual y la culpabilidad de la teoría macroeconómica," Revista de Economía Institucional, Universidad Externado de Colombia - Facultad de Economía, vol. 12(22), pages 111-128, January-J.
- Dominique Guégan & Wayne Tarrant, 2012.
"On the necessity of five risk measures,"
Annals of Finance, Springer, vol. 8(4), pages 533-552, November.
- Dominique Guegan & Wayne Tarrant, 2010. "On the necessity of five risk measures," Documents de travail du Centre d'Economie de la Sorbonne 10005, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
- Dominique Guegan & Wayne Tarrant, 2012. "On the Necessity of Five Risk Measures," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00721339, HAL.
- Dominique Guegan & Wayne Tarrant, 2010. "On the necessity of five risk measures," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00460901, HAL.
- Alagidede, Paul & Panagiotidis, Theodore, 2009.
"Modelling stock returns in Africa's emerging equity markets,"
International Review of Financial Analysis, Elsevier, vol. 18(1-2), pages 1-11, March.
- Paul Alagidede & Theodore Panagiotidis, 2009. "Modelling stock returns in Africa’s emerging equity markets," Discussion Paper Series 2009_01, Department of Economics, University of Macedonia, revised Jan 2009.
- Alagidede, Paul & Panagiotidis, Theodore, 2009. "Modelling stock returns in Africa's emerging equity markets," Stirling Economics Discussion Papers 2009-04, University of Stirling, Division of Economics.
- Ben Klemens, 2013. "A Peer-based Model of Fat-tailed Outcomes," Papers 1304.0718, arXiv.org.
- Lombardi, Marco J. & Calzolari, Giorgio, 2009.
"Indirect estimation of [alpha]-stable stochastic volatility models,"
Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
- Marco Lombardi & Giorgio Calzolari, 2006. "Indirect estimation of alpha-stable stochastic volatility models," Econometrics Working Papers Archive wp2006_07, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
- Geluk, J.L. & De Vries, C.G., 2006.
"Weighted sums of subexponential random variables and asymptotic dependence between returns on reinsurance equities,"
Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 39-56, February.
- J.L. Geluk & C.G. de Vries, 2004. "Weighted Sums of Subexponential Random Variables and Asymptotic Dependence between Returns on Reinsurance Equities," Tinbergen Institute Discussion Papers 04-102/2, Tinbergen Institute.
- Geluk, J.L. & de Vries, C.G., 2004. "Weighted sums of subexponential random variables and asymptotic dependence between returns on reinsurance equities," Econometric Institute Research Papers EI 2004-47, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- Erie Febrian & Aldrin Herwany, 2009.
"Volatility Forecasting Models and Market Co-Integration: A Study on South-East Asian Markets,"
Working Papers in Economics and Development Studies (WoPEDS)
200911, Department of Economics, Padjadjaran University, revised Sep 2009.
- Erie Febrian & Aldrin Herwany, 2010. "Volatility Forecasting Models and Market Co-Integration: A Study on South-East Asian Markets," Working Papers in Business, Management and Finance 201005, Department of Management and Business, Padjadjaran University, revised May 2010.
- Vianna Franco, Marco P. & Ribeiro, Leonardo Costa & Albuquerque, Eduardo da Motta e, 2022.
"Beyond Random Causes: Harmonic Analysis Of Business Cycles At The Moscow Conjuncture Institute,"
Journal of the History of Economic Thought, Cambridge University Press, vol. 44(3), pages 456-476, September.
- Franco, Marco Paulo Vianna & Ribeiro, Leonardo Costa & da Motta e Albuquerque, Eduardo, 2021. "Beyond Random Causes: Harmonic Analyis of Business Cycles at the Moscow Conjuncture Institute," OSF Preprints 6aesk, Center for Open Science.
- de Lima, Pedro J. F., 1997. "On the robustness of nonlinearity tests to moment condition failure," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 251-280.
- P. Kearns & A.R. Pagan, 1993.
"Australian Stock Market Volatility: 1875–1987,"
The Economic Record, The Economic Society of Australia, vol. 69(2), pages 163-178, June.
- Pagan, A.R. & Kearns, P., 1990. "Ustralian Stock Market Volatility: 1875-1987," RCER Working Papers 248, University of Rochester - Center for Economic Research (RCER).
- Igor Fedotenkov, 2020.
"A Review of More than One Hundred Pareto-Tail Index Estimators,"
Statistica, Department of Statistics, University of Bologna, vol. 80(3), pages 245-299.
- Fedotenkov, Igor, 2018. "A review of more than one hundred Pareto-tail index estimators," MPRA Paper 90072, University Library of Munich, Germany.
- Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
- Runde, Ralf & Scheffner, Axel, 1998. "On the existence of moments: With an application to German stock returns," Technical Reports 1998,25, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
More about this item
Keywords
Stochastic differential equations (SDEs); Chebyshev cardinal wavelets (CCWs); Variable-order fractional Brownian motion (V-Ofbm); Stochastic Lotka–Volterra system; Stochastic Brusselator problem; Stochastic Duffing-Van der Pol oscillator problem; Stochastic pendulum model;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:124:y:2019:i:c:p:105-124. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.