Allow me one further 'make or break my reputation with Laurent' conjecture...
For .
No worry for your reputation .
By the way, one of the definitions of Brownian motion is: a continuous centered Gaussian process ( , is a centered Gaussian r.v.) with covariance for all .
By the way, one of the definitions of Brownian motion is: a continuous centered Gaussian process ( , is a centered Gaussian r.v.) with covariance for all .