# Statistical Differential Equation

1. Nov 5, 2013

### fuchs

Stochastic Differential Equation

Hi there,
I am trying to solve (analytically) a stochastic differential equation of the form:
$\frac{d^2}{dt^2}x +\left(k(t)+\delta k \ t\right)x)=0$

Here \delta k is a random (gaussian) white noise. Note, that in the differential equation it is multiplied by t which makes this equation hard to solve.

I would like to calculate <x(t)> and <x(t)^2>. Any suggestion what formulas I could use? Unfortunately I never had a lecture in SDE.

Last edited: Nov 5, 2013