: Multiple editions and related foundational papers, including "Stochastic Processes and Statistics," are available for download with a subscription or account on Hardcopy & Purchasing
: A detailed review and partial introduction of the 1953 Wiley edition are available as a free PDF download . stochastic process doob pdf download install
Unlocking the Foundation: Joseph L. Doob’s "Stochastic Processes" including "Stochastic Processes and Statistics
[ E[M_n - M_n-1 | \mathcalF n-1] = E[X_n - A_n - X n-1 + A_n-1 | \mathcalF n-1] ] But (A_n - A n-1 = E[X_n - X_n-1 | \mathcalF_n-1]), so the right-hand side is zero. Uniqueness follows from the fact that any such decomposition forces (A) to be defined as above. stochastic process doob pdf download install