Product expansion for stochastic jump diffusions and its application to numerical approximation
✍ Scribed by X.Q. Liu; C.W. Li
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 184 KB
- Volume
- 108
- Category
- Article
- ISSN
- 0377-0427
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✦ Synopsis
We derive a product expansion of the exponential Lie series in terms of a Philip Hall basis for the Chen series corresponding to the stochastic jump di usion as in Sussmann (in: C.I. Byrnes and A. Lindquist (Eds.), Theory and Applications of Nonlinear Control Systems, North-Holland, Amsterdam, 1986, pp. 323-335) for the deterministic case. Based on the expansion, we establish the Stratonovich-Taylor-Hall (STH) schemes such that each scheme involves only the minimum number of multiple stochastic integrals, which can be regarded as systems of stochastic di erential equations and approximated by a lower order scheme with an appropriate step size to ensure the necessary accuracy. Mean-square convergence of the STH schemes is shown and numerical examples are provided to illustrate the results.