Stochastic differential equacions

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Hello

I would love to know the basics of how to solve stochastic differential equations. Also what importance does the Ito integral lend to this matter?

Thanks for any help!
 

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Stochastic Systems

Stochastic differential equations are typical differential equations with a random variable added to it. A classic example would be a stochastic harmonic oscillator. [itex]\frac{{d^2 x}}{{dt^2 }} + \frac{b}{m} \cdot \frac{{dx}}{{dt}} + \omega _0 \cdot x - \varepsilon (t) = f(t)[/itex] the part [itex] \varepsilon (t) [/itex] is the random component, b is the damping factor, m is the mass and [itex] \omega _0 [/itex] is the angular frequency. The difficult part of understanding the stochastic systems is not the systems part but the stochastic part. To accurately model a stochastic system requires a good knowledge of the statistics of the random component. Accurately modeling noise if difficult. Some things you may want to research are time series modeling (SARIMA, ARIMA and decomposition methods, spectral analysis) you could also research langevin (I think I spelled that right) mechanics and several aspects of modern statistical physics.
 
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