If we have a DE of the following form:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{dX}{dt}=b(t,X_t)+\sigma(t,X_t).W_t[/tex]

and look for a stochastic process to represent the (second) noise term. Now my textbook tells me that the only process with 'continuous paths' is Brownian motion.

The noise term denotes random, indeterministic behaviour in the physical situation the DE is modelling.

Can someone please explain why is this is the case, and why it is significant?

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# Stochastic Differential Equations

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