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Stability of weak numerical schemes for stochastic differential equations

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  • Hofmann, Norbert

Abstract

We consider numerical stability and convergence of weak schemes solving stochastic differential equations. A relatively strong notion of stability for a special type of test equations is proposed. These are stochastic differential equations with multiplicative noise. For explicit and implicit Euler schemes the regions of stability are also examined.

Suggested Citation

  • Hofmann, Norbert, 1995. "Stability of weak numerical schemes for stochastic differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 38(1), pages 63-68.
    • Handle: RePEc:eee:matcom:v:38:y:1995:i:1:p:63-68
    DOI: 10.1016/0378-4754(93)E0067-F
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    1. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187, July.
    2. P. E. Kloeden & Eckhard Platen, 1992. "Higher-order implicit strong numerical schemes for stochastic differential equations," Published Paper Series 1992-1, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
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    Cited by:

    1. Wu, Shujin & Han, Dong, 2007. "Algorithmic analysis of Euler scheme for a class of stochastic differential equations with jumps," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 211-219, January.

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