Herein, we describe multidimensional Brownian motions for d = 2; 3 with drifts whose order is the same as that of the mean displacement of a Brownian motion. We consider the probabilities that the processes remain in specific cones for a considerable amount of time. We obtain exponents expressing the probabilities, which are different from that of the ordinary Brownian motion. Finally, we suggest an open problem concerning the exact values.
All Science Journal Classification (ASJC) codes
- Statistics and Probability