Stochastic Calculus: Martingale

[Win_odd Dhamnekar]

Note: This example is taken from the book titled " Stochastic Calculus: An Introduction with Applications" written by Gregory F.Lawler.





In the above example how
is compted by author from the previous step?

In my opinion, it should be $$\mathbb{E}([|W_n|]) \leq \displaystyle\sum_{j=1}^n K_j (\mathbb{E}[|M_j|] - \mathbb{E}[|M_{j-1}|]) < \infty$$ Is my opinion correct?

 

[Dr.Peterson]

In the above example how
View attachment 34996 is computed by author from the previous step?

In my opinion, it should be $$\mathbb{E}([|W_n|]) \leq \displaystyle\sum_{j=1}^n K_j (\mathbb{E}[|M_j|] - \mathbb{E}[|M_{j-1}|]) < \infty$$ Is my opinion correct?

Please explain the reason for your opinion. This looks like the triangle inequality to me ...

 

[Win_odd Dhamnekar]

Please explain the reason for your opinion. This looks like the triangle inequality to me ...

I think author is correct. (Why??? )