Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Suppose X_1,X_2,...,X_n are n Brownian motions with respect to the same filtration such that X_1 is independent of X_j for all j=2,...,n. Is it true that X_1 is independent of (X_2,...,X_n)?

share|improve this question
add comment

1 Answer 1

This is clearly false. Take X independent of Y and Z=integral of sgn(X_s)dY_s. Then if your result is true we would have X independent of the cross vriation of Y and Z which is integral of sgn(X_s)ds. This is false.

share|improve this answer
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.