Mixed fractional Brownian sheets and their applications

作者：Wu Dongsheng^*

来源：Journal of Mathematical Physics, 2011, 52(6): 063510.

DOI：10.1063/1.3598421

Let X={X(t), t is an element of R(+)(N)} be an (N, d)-mixed fractional Brownian sheet, that is, X(t) = B(alpha)(t) + aB(beta)(t) for all t is an element of R(+)(N), where B(alpha) and B(beta) are two independent (N, d)-fractional Brownian sheets with Hurst indices alpha = (alpha(1), ... ,alpha(N)) is an element of (0, 1)(N) and beta = (beta(1), ... ,beta(N)) is an element of (0, 1)(N), respectively, and where a is an element of R is a nonzero constant. In this paper, we obtain the Hausdorff and packing dimensions of the range X([0, 1](N)), the graph GrX([0, 1](N)), and the level sets for the mixed fractional Brownian sheet X. We then establish the exact uniform and local moduli of continuity for the real-valued mixed fractional Brownian sheet X(0). As an application, we study the regularity of the collision local times of two independent fractional Brownian sheets and provide a sufficient condition for the collision local times having a joint continuous version. We also determine the Hausdorff and packing dimensions of the set of collision times.

• 出版日期2011-6