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Almost sure stability of the Euler–Maruyama method with random variable stepsize for stochastic differential equations
- Source :
- Numerical Algorithms. 74:573-592
- Publication Year :
- 2016
- Publisher :
- Springer Science and Business Media LLC, 2016.
-
Abstract
- In this paper, the Euler---Maruyama (EM) method with random variable stepsize is studied to reproduce the almost sure stability of the true solutions of stochastic differential equations. Since the choice of the time step is based on the current state of the solution, the time variable is proved to be a stopping time. Then the semimartingale convergence theory is employed to obtain the almost sure stability of the random variable stepsize EM solution. To our best knowledge, this is the first paper to apply the random variable stepsize (with clear proof of the stopping time) to the analysis of the almost sure stability of the EM method.
- Subjects :
- Applied Mathematics
Numerical analysis
Mathematical analysis
010103 numerical & computational mathematics
Adaptive stepsize
01 natural sciences
Stability (probability)
Euler–Maruyama method
Mathematics::Numerical Analysis
010101 applied mathematics
Stochastic differential equation
Semimartingale
Stopping time
Computer Science::Multimedia
0101 mathematics
QA
Random variable
Mathematics
Subjects
Details
- ISSN :
- 15729265 and 10171398
- Volume :
- 74
- Database :
- OpenAIRE
- Journal :
- Numerical Algorithms
- Accession number :
- edsair.doi.dedup.....b33b888991267dcb6244e20818a11b65