Abstract
AbstractIn this paper, we analyze the drift-implicit (or backward) Euler numerical scheme for a class of stochastic differential equations with unbounded drift driven by an arbitraryλ-Hölder continuous process,λ∈ (0,1). We prove that, under some mild moment assumptions on the Hölder constant of the noise, the$L^{r}({\Omega };L^{\infty }([0,T]))$Lr(Ω;L∞([0,T]))-approximation error converges to 0 asO(Δλ), Δ → 0. To exemplify, we consider numerical schemes for the generalized Cox–Ingersoll–Ross and Tsallis–Stariolo–Borland models. The results are illustrated by simulations.
Funder
Norges Forskningsråd
Core Research for Evolutional Science and Technology
University of Oslo
Publisher
Springer Science and Business Media LLC
Reference22 articles.
1. Alfi, V., Coccetti, F., Petri, A., Pietronero, L.: Roughness and finite size effect in the NYSE stock-price fluctuations. The European Phys. J. B 55(2), 135–142 (2007)
2. Alfonsi, A.: On the discretization schemes for the CIR (and Bessel squared) processes. Monte Carlo Methods Appl. 11(4), 355–384 (2005)
3. Alfonsi, A.: Strong order one convergence of a drift implicit Euler scheme: application to the CIR process. Statist. Probab. Lett. 83(2), 602–607 (2013)
4. Andersen, L. B. G., Piterbarg, V. V.: Moment explosions in stochastic volatility models. Finance Stochast. 11(1), 29–50 (2006)
5. Ayache, A., Cohen, S., Vehel, J. L.: The covariance structure of multifractional Brownian motion, with application to long range dependence. In: 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100), IEEE (2002)
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