WFRF:(Lansky Petr)
Search: WFRF:(Lansky Petr) > Qualitative propert...
- 1 of 1
- Previous record
- Next record
- To hitlist
- Tubikanec, IreneJohannes-Kepler-University of Linz (author)
Qualitative properties of different numerical methods for the inhomogeneous geometric Brownian motion
- Article/chapterEnglish2022
Publisher, publication year, extent ...
- Elsevier BV,2022
Numbers
- LIBRIS-ID:oai:lup.lub.lu.se:b46ff588-c5a4-4799-b872-73a75967ee7a
- https://lup.lub.lu.se/record/b46ff588-c5a4-4799-b872-73a75967ee7aURI
- https://doi.org/10.1016/j.cam.2021.113951DOI
Supplementary language notes
- Language:English
- Summary in:English
Part of subdatabase
- SwePubSwePub
Classification
Notes
- We provide a comparative analysis of qualitative features of different numerical methods for the inhomogeneous geometric Brownian motion (IGBM). The limit distribution of the IGBM exists, its conditional and asymptotic mean and variance are known and the process can be characterised according to Feller's boundary classification. We compare the frequently used Euler–Maruyama and Milstein methods, two Lie–Trotter and two Strang splitting schemes and two methods based on the ordinary differential equation (ODE) approach, namely the classical Wong–Zakai approximation and the recently proposed log-ODE scheme. First, we prove that, in contrast to the Euler–Maruyama and Milstein schemes, the splitting and ODE schemes preserve the boundary properties of the process, independently of the choice of the time discretisation step. Second, we prove that the limit distribution of the splitting and ODE methods exists for all stepsize values and parameters. Third, we derive closed-form expressions for the conditional and asymptotic means and variances of all considered schemes and analyse the resulting biases. While the Euler–Maruyama and Milstein schemes are the only methods which may have an asymptotically unbiased mean, the splitting and ODE schemes perform better in terms of variance preservation. The Strang schemes outperform the Lie–Trotter splittings, and the log-ODE scheme the classical ODE method. The mean and variance biases of the log-ODE scheme are very small for many relevant parameter settings. However, in some situations the two derived Strang splittings may be a better alternative, one of them requiring considerably less computational effort than the log-ODE method. The proposed analysis may be carried out in a similar fashion on other numerical methods and stochastic differential equations with comparable features.
Subject headings and genre
- NATURVETENSKAP Matematik Beräkningsmatematik hsv//swe
- NATURAL SCIENCES Mathematics Computational Mathematics hsv//eng
- Boundary preservation
- Feller's boundary classification
- GARCH model
- Log-ODE method
- Moment preservation
- Numerical splitting schemes
Added entries (persons, corporate bodies, meetings, titles ...)
- Tamborrino, MassimilianoUniversity of Warwick (author)
- Lansky, PetrInstitute of Physiology of the Academy of Sciences of the Czech Republic (author)
- Buckwar, EvelynLund University,Lunds universitet,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH,Johannes-Kepler-University of Linz(Swepub:lu)ev5875bu (author)
- Johannes-Kepler-University of LinzUniversity of Warwick (creator_code:org_t)
Related titles
- In:Journal of Computational and Applied Mathematics: Elsevier BV4060377-0427
Internet link
Find in a library
- Journal of Computational and Applied Mathematics (Search for host publication in LIBRIS)
To the university's database
- 1 of 1
- Previous record
- Next record
- To hitlist
Find more in SwePub
- By the author/editor
- Tubikanec, Irene
- Tamborrino, Mass ...
- Lansky, Petr
- Buckwar, Evelyn
- About the subject
-
- NATURAL SCIENCES
- NATURAL SCIENCES
- and Mathematics
- and Computational Ma ...
- Articles in the publication
- Journal of Compu ...
- By the university
- Lund University
Search outside SwePub
- Extend your search to:
- Google Book Search
- Google Scholar
Kungliga biblioteket hanterar dina personuppgifter i enlighet med EU:s dataskyddsförordning (2018), GDPR. Läs mer om hur det funkar här.
Så här hanterar KB dina uppgifter vid användning av denna tjänst.
- Copyright © LIBRIS - National Library Systems
- LIBRIS.kb.se
