Some results on fractional Brownian sheets and their local times
Let \(B^H_0=\{ B^H_0(t), t\in\mathbb R_+^N\}\) be a real-valued fractional Brownian sheet. Define the \((N, d)\)-Gaussian random field \(B^H\) by \[ B^H(t)= (B^H_1(t),\dots, B^H_d(t)), \quad t \in\mathbb R^N_+, \] where \(B^H_1,\dots,B^H_d\) are independent copies of \(B_0^H\). The existence and joint continuity of local times of \(B^H\) is proven in some given conditions in [\textit{Y. Xiao} and \textit{T. Zhang}, Probab. Theory Relat. Fields 124, No.~2, 204--226 (2002; Zbl 1009.60024)]. The authors study further properties of the local times of \(B^H\), such as the moments of increments of local times, the large increments and the maximum moduli of continuity of local times and as a result, we answer the questions posed in [loc. cit.].
scientific article; zbMATH DE number 5357873