Prove (2.9), that is, that and that Assume that the processes With M10 = M20 = 0, are martingales with respect to the history The predictable covariation process is for defined by While ...

Prove (2.9), that is, that

and that

Assume that the processes

With M₁₀
= M₂₀
= 0, are martingales with respect to the history

The predictable covariation process

is for

defined by

While

The optional covariation process

is defined by

For

a) Show that

are mean zero martingales.

b) Show that

for all n.