Stochastic Differential Equation

[hzzhangyu]

Homework Statement

How to solve this SDE?

dX_t = [1/X_t] dt + aX_t dB_t

Homework Equations

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!

 

[gabbagabbahey]

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

 

[Dickfore]

Try the substitution

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