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math.PR2015★ 50 cited
The exponential Lie series for continuous semimartingales
Kurusch Ebrahimi-Fard, Simon J. A. Malham, Frederic Patras +1
We consider stochastic differential systems driven by continuous semimartingales and governed by non-commuting vector fields. We prove that the logarithm of the flowmap is an expon…
math.PR2015★ 18 cited
Flows and stochastic Taylor series in Ito calculus
Kurusch Ebrahimi-Fard, Simon J. A. Malham, Frederic Patras +1
For stochastic systems driven by continuous semimartingales an explicit formula for the logarithm of the Ito flow map is given. A similar formula is also obtained for solutions of…