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Recently Referred Formulae

{\rm d}v &=& ae^{at}u {\rm d}t   e^{at}{\rm d}u\\
&=& ae^{at}u {\rm d}t   e^{at}(-au{\rm d}t - \sigma{\rm d}W_t)\\
&=& -\sigma e^{at}{\rm d}W_t
{\rm d}y(t) &=& \frac{\partial g}{\partial t}{\rm d}t   \frac{\partial g}{\partial x}{\rm d}x   \frac{1}{2}\frac{\partial^2 g}{\partial x^2}({\rm d}x)^2
y(t) &=& y(0)   (\mu - \frac{1}{2}\sigma^2)t   \sigma W(t) \\
x(t) &=& x(0)\exp\left( (\mu - \frac{1}{2}\sigma^2)t   \sigma W(t) \right)
{\rm d}x(t) &=& a(x, t){\rm d}t   b(x, t){\rm d}W_t\\
y(t) &=& g(x, t)
r(t) = r(0)e^{-at}   b(1-e^{-at})   \sigma e^{-at}\int_{0}^{t}e^{as}{\rm d}W_s