Table of Ito Integrals Are there any tables with a collection of common Ito Integrals, their equivalent forms, etc. that anyone knows of?
Did a search but didn't come up with anything and was wondering if anyone knew of anything of the like...
Thanks.
 A: $\newcommand{\d}{\mathrm{d}}$Here is a short list of useful correspondences, especially for certain useful martingales such as $e^{B_t - \tfrac{1}{2}t}$:
\begin{array} {|r|r|}
\hline
X_t     & \d X_t = u \d t + v \d B_t\\ \hline 
  B_t     & \d B_t\\ 
  B_t^2   & 2 B_t \d B_t + \d t\\ 
  B_t^2 - t & 2 B_t \d B_t\\ 
  B_t^3   & 3 B_t^2 \d B_t + 3 B_t \d t\\ 
  e^{B_t} & e^{B_t}\d B_t + \tfrac{1}{2}e^{B_t}\d t \\
  e^{B_t - \tfrac{1}{2}t} & e^{B_t - \tfrac{1}{2}t} \d B_t\\
  e^{\tfrac{1}{2}t}\sin B_t & e^{\tfrac{1}{2}t} \cos B_t \d B_t\\
  e^{\tfrac{1}{2}t}\cos B_t & -e^{\tfrac{1}{2}t} \sin B_t \d B_t\\
  (B_t + t) e^{-B_t - \tfrac{1}{2}t} & (1 - B_t - t) e^{-B_t - \tfrac{1}{2}t} \d B_t\\\hline
\end{array}
All the above can be verified using Itô's formula and alongside the Itô isometry and integration by parts can be used to evaluate several stochastic integrals, their expectations and variances. 
Here is a table of stochastic integrals...
\begin{array} {|r|r|r|}
\hline
\text{Stochastic Integral}     & \text{Result} & \text{Variance}\\ \hline 
 \int_0^t \d B_s        & B_t                      & t \\
 \int_0^t s \d B_s      & tB_t - \int_0^t B_s \d s & \tfrac{1}{3}t^3 \\ 
 \int_0^t B_s \d B_s    & \tfrac{1}{2}B_t^2 - \tfrac{1}{2}t & \tfrac{1}{2}t^2\\
 \int_0^t B_s^2 \d B_s  & \tfrac{1}{3}B_t^3 - \int_0^t B_s \d s& 3t^2\\
 \int_0^t e^{B_s - \tfrac{1}{2}s}\d B_s 
    & e^{B_t - \tfrac{1}{2}t} - 1 
    & e^{t}-1\\
\hline
\end{array}
A: This actually isn't a bad start anyway if anyone is looking for the same...
Stochastic Calculus Cheat Sheet
