Determine if process is a martingale

 

Determine if the following process is a martingale

 

Y(t) = wX1(t) + Sqrt(1-w2)X2(t)

 

Where X1(t)  & X2(t)  are independent. and are brownian motion.

assume Y(t) satisfys the integrability condition. 

 

Also answer following : Does answer depend on w? what is possible definition of w?, will Y(t) keep the properties of Brownian motion.

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