Finding the Quadratic Variation Process

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Let $X = X_t$ be an ito process

$X_t = X_0 + \frac{1}{3}t^3+\int_0^t e^s dB_s , t \geq 0$

and let $Y = Y_t$ also be an ito process

$Y_t = Y_0 + te^t+\int_0^t s^2 dB_s ,t \geq 0$

How would I find the Quadratic Variation process $\langle X^2+Y^2 , XY \rangle$?

From what I understand I will need to apply Ito's formula at some point but my issue is i'm not quite sure when I need to apply Ito's formula.

This is much more complicated than other examples we have covered in class so any help is massively appreciated! :)