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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2014 • Question 2

Question

Math 6010 • Linear Models Fall 2014 • Question 2

Suppose \(\{X_n\}_{n=1}^{\infty }\) and \(\{Y_n\}_{n=1}^{\infty }\) are submartingales with respect to the same filtration \(\{\mathcal {F}_n\}_{n=1}^{\infty }\). Prove that \(Z_n:=\max (X_n,Y_n)\) is also a submartingale.

Raw LaTeX

Suppose \(\{X_n\}_{n=1}^{\infty}\) and
\(\{Y_n\}_{n=1}^{\infty}\) are submartingales with respect to the same
filtration \(\{\mathcal{F}_n\}_{n=1}^{\infty}\). Prove that
\(Z_n:=\max(X_n,Y_n)\) is also a submartingale.

Topic Tags

Filtrations and Stopping Times Martingales and Supermartingales Uniform Integrability and Truncation Methods