ON THE ALMOST SURE CONVERGENCE OF THE SQUARE VARIATION
OF THE BROWNIAN MOTION
Abstract: The paper deals with the problem of almost sure (a.s.) convergence of the square
variation of the Brownian motion when the diameters of partitions of the time interval
tend to zero. It is known that if the diameters converge fast enough, namely if is of
order less than , then a.s. convergence takes place. On the other hand, we
show that there exists a sequence of partitions with diameters of order less
than for any such that the Brownian square variation diverges
a.s.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -