On weak Brownian motions of arbitrary order. (English) Zbl 0968.60069

Föllmer, Hans; Wu, Ching-Tang; Yor, Marc

Ann. Inst. Henri Poincaré, Probab. Stat. 36, No. 4, 447-487 (2000).

A weak Brownian motion of order \(k\) is a stochastic process having the same \(k\)-dimensional marginals as Brownian motion. The authors prove the existence of continuous weak Brownian motions of any order; this is done with the corresponding law on Wiener space both equivalent or singular to Wiener measure. Moreover, they show that there are even weak Brownian motions whose law coincides with Wiener measure outside of any interval of length \(\varepsilon\).

Reviewer: Martin Schweizer (Berlin)

MSC:

60J65	Brownian motion
45D05	Volterra integral equations
60G15	Gaussian processes
60G48	Generalizations of martingales

Keywords:

weak Brownian motion; marginal distributions; Wiener measure; Brownian motion; Volterra kernel