Proceedings of the Korean Statistical Society Conference (한국통계학회:학술대회논문집)
- 2003.05a
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- Pages.25-30
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- 2003
Lie Algebraic Solution of Stochastic Differential Equations
- Kim, Yoon-Tae (Hallym University) ;
- Jeon, Jong-Woo (Seoul National University)
- Published : 2003.05.23
Abstract
We prove that the logarithm of the flow of stochastic differential equations is an element of the free Lie algebra generated by a finite set consisting of vector fields being coefficients of equations. As an application, we directly obtain a formula of the solution of stochastic differential equations given by Castell(1993) without appealing to an expansion for ordinary differential equations given by Strichartz (1987).
Keywords
- Lie algebra;
- Specht-Wever theorem;
- iterated Stratonovich integral;
- Lie bracket;
- Stochastic differential equation