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$dY_1 =\beta_1dt +1dB_1+2dB_2+3dB_3$

$dY_2 =\beta_2dt +1dB_1+2dB_2+2dB_3$

$\beta_{1,2} $ bounded, $B_{1,2,3}$ Brownian Motions.

System of SDEs.

I know how to solve a linear SDE with 1 Brownian motion.

I can (or at least think) solve a system of $n\times n$ linear SDEs.

But what am I supposed to do with 3 different Brownian Motions?

JonesY
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    I don't see an SDE in your question... these two are just Itô processes given in their differential form, e.g. $$Y_1(t) = Y_1(0) + \int_0^t \beta_1(s) , ds+ B_1(t)+2B_2(t)+3B_3(t)$$ – saz Jul 31 '16 at 18:11

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Indeed as mentioned in the comments, these are simply two correlated Itô diffusions since they have common Brownian motion noise, which you can actually combine into single Brownian motion $\sqrt{1+2^{2}+3^{2}}B_{t}=\sqrt{14}B_{t}.$

Thomas Kojar
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