Product rule of stochastic exponents

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we know that for standard exponents, $(e^x)(e^y)=e^{(x+y)}$. What is the product rule for stochastic exponents?

$E_n(U)E_n(V)=E_n(U+V+[U,V])$ where $U$ and $V$ are stocchastic sequences, $E_n$ is the stochastic exponent and $[U,V]_n$=$ \sum_{k=1}^n(\Delta_Uk*\Delta_Vk)$.

That is the rule, but whats the proof!? thx :)