V: 18, 191-195, LNM 191 (1971)
MEYER, Paul-André
Démonstration simplifiée d'un théorème de Knight (
Martingale theory)
A well known theorem (Dambis, Dubins) asserts that a continuous martingale reduces to Brownian motion when time-changed by its own increasing process. Knight's theorem (LN in M
190) asserts that this operation performed on $n$ orthogonal martingales yields $n$ independent Brownian motions. The result is extended to Poisson processes
Comment: Still simpler proofs can be given, see
1448 (included in Revuz-Yor
Continuous Martingales and Brownian Motion, Chapter V)
Keywords: Continuous martingales,
Changes of timeNature: Exposition,
Original additions
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