Exact Rate of Convergence of Some Approximation Schemes Associated to SDEs Driven by a Fractional Brownian Motion
Author
Abstract
Suggested Citation
DOI: 10.1007/s10959-007-0083-0
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
- Benassi, Albert & Cohen, Serge & Istas, Jacques & Jaffard, Stéphane, 1998. "Identification of filtered white noises," Stochastic Processes and their Applications, Elsevier, vol. 75(1), pages 31-49, June.
- Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
- Coeurjolly, Jean-Francois, 2000. "Simulation and identification of the fractional Brownian motion: a bibliographical and comparative study," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 5(i07).
- Nourdin, Ivan & Simon, Thomas, 2006. "On the absolute continuity of one-dimensional SDEs driven by a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 907-912, May.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Nicholas Ma & David Nualart, 2020. "Rate of Convergence for the Weighted Hermite Variations of the Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 33(4), pages 1919-1947, December.
- Ivan Nourdin & David Nualart, 2010. "Central Limit Theorems for Multiple Skorokhod Integrals," Journal of Theoretical Probability, Springer, vol. 23(1), pages 39-64, March.
- Orimar Sauri, 2024. "Asymptotic Error Distribution of the Euler Scheme for Fractional Stochastic Delay Differential Equations with Additive Noise," Papers 2402.08513, arXiv.org.
- Héctor Araya & Jorge A. León & Soledad Torres, 2020. "Numerical Scheme for Stochastic Differential Equations Driven by Fractional Brownian Motion with $$ 1/4," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1211-1237, September.
- Nobuaki Naganuma, 2015. "Asymptotic Error Distributions of the Crank–Nicholson Scheme for SDEs Driven by Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 28(3), pages 1082-1124, September.
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.- Bégyn, Arnaud, 2007. "Functional limit theorems for generalized quadratic variations of Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1848-1869, December.
- Bibinger, Markus, 2020. "Cusum tests for changes in the Hurst exponent and volatility of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 161(C).
- Kubilius, K. & Mishura, Y., 2012. "The rate of convergence of Hurst index estimate for the stochastic differential equation," Stochastic Processes and their Applications, Elsevier, vol. 122(11), pages 3718-3739.
- Marco Dozzi & Yuliya Mishura & Georgiy Shevchenko, 2015. "Asymptotic behavior of mixed power variations and statistical estimation in mixed models," Statistical Inference for Stochastic Processes, Springer, vol. 18(2), pages 151-175, July.
- Neuenkirch, Andreas, 2008. "Optimal pointwise approximation of stochastic differential equations driven by fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2294-2333, December.
- Kerstin Gärtner & Mark Podolskij, 2014. "On non-standard limits of Brownian semi-stationary," CREATES Research Papers 2014-50, Department of Economics and Business Economics, Aarhus University.
- Surgailis, Donatas & Teyssière, Gilles & Vaiciulis, Marijus, 2008. "The increment ratio statistic," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 510-541, March.
- Bai, Shuyang & Taqqu, Murad S. & Zhang, Ting, 2016. "A unified approach to self-normalized block sampling," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2465-2493.
- John-Fritz Thony & Jean Vaillant, 2022. "Parameter Estimation for a Fractional Black–Scholes Model with Jumps from Discrete Time Observations," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
- Ayache, Antoine & Lévy Véhel, Jacques, 2004. "On the identification of the pointwise Hölder exponent of the generalized multifractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 119-156, May.
- Shuyang Bai & Murad S. Taqqu, 2013. "Multivariate Limit Theorems In The Context Of Long-Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 717-743, November.
- Fan, XiLiang, 2015. "Logarithmic Sobolev inequalities for fractional diffusion," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 165-172.
- Miguel A. Arcones, 1999. "The Law of the Iterated Logarithm over a Stationary Gaussian Sequence of Random Vectors," Journal of Theoretical Probability, Springer, vol. 12(3), pages 615-641, July.
- Marina Resta & Davide Sciutti, 2003. "Spot price dynamics in deregulated power markets," Econometrics 0312002, University Library of Munich, Germany.
- Jean-Christophe Breton & Jean-François Coeurjolly, 2012. "Confidence intervals for the Hurst parameter of a fractional Brownian motion based on finite sample size," Statistical Inference for Stochastic Processes, Springer, vol. 15(1), pages 1-26, April.
- Bondarenko, Valeria & Bondarenko, Victor & Truskovskyi, Kyryl, 2017. "Forecasting of time data with using fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 97(C), pages 44-50.
- Ahmadian, D. & Ballestra, L.V., 2020. "Pricing geometric Asian rainbow options under the mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
- Sinn, Mathieu & Keller, Karsten, 2011. "Estimation of ordinal pattern probabilities in Gaussian processes with stationary increments," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1781-1790, April.
- Kozachenko Yuriy & Pashko Anatolii & Vasylyk Olga, 2018. "Simulation of generalized fractional Brownian motion in C([0,T])," Monte Carlo Methods and Applications, De Gruyter, vol. 24(3), pages 179-192, September.
- Nourdin, Ivan & Nualart, David & Peccati, Giovanni, 2021. "The Breuer–Major theorem in total variation: Improved rates under minimal regularity," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 1-20.
More about this item
Keywords
Fractional Brownian motion; Russo-Vallois integrals; Doss-Sussmann type transformation; Stochastic differential equations; Euler scheme; Crank-Nicholson scheme; Mixing law;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:spr:jotpro:v:20:y:2007:i:4:d:10.1007_s10959-007-0083-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.