# Stochastic Differential Equation

1. May 13, 2010

### hzzhangyu

1. The problem statement, all variables and given/known data

How to solve this SDE?

dX_t = [1/X_t] dt + aX_t dB_t

2. Relevant equations

3. The attempt at a solution

If I didnt get it wrong, this is not a general linear SDE, and my course in elementary stochastic calcus did not cover SDEs other than the general linear ones. Thanks for the help!

2. May 13, 2010

### gabbagabbahey

It definitely looks non-linear, but it might be reducible into a linear SDE.

3. May 13, 2010

### Dickfore

Try the substitution

$$Z_{t} = X^{2}_{t}$$