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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2008 • Question 1

Question

Math 6010 • Linear Models Fall 2008 • Question 1

Let \(X_1,X_2,\ldots \) be random variables such that the partial sums \(S_n:=X_1+X_2+\cdots +X_n\) determine a martingale. Show that \(\mathbb {E}[X_iX_j]=0\) if \(i\neq j\).

Raw LaTeX

Let \(X_1,X_2,\ldots\) be random variables such that the partial sums
\(S_n:=X_1+X_2+\cdots+X_n\) determine a martingale. Show that
\(\E[X_iX_j]=0\) if \(i\neq j\).

Topic Tags

Exponential Martingales Infinite Products and Multiplicative Martingales Martingales and Supermartingales Uniform Integrability and Truncation Methods