Let me consider harmonic oscillations x'' + x = f_t(t), where f_t(t) describes thermal stochastic force
All this and more is described in van Kampen’s book ``Stochastic processes in physics and chemistry".
Introduction to Stochastic Calculus for Finance: A New Didactic Approach (Lecture Notes in Economics and Mathematical Systems)
Dieter Sondermann
This can be helpful.
The most gentle introduction I've ever seen is S. Stepanov, Stochastic World. Then you may switch to B. Oksendal, Stochastic differential equations.
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