Abstract
Let {B̂H(t)(t)}={B̂H(t)(t),t∊R+N} be an (N,d)-multifractional Brownian sheet with N Hurst functionals Hℓ(tℓ)∊CKℓ(R+,(0,1)) for some Kℓ∊(0,1)(ℓ=1,…,N) defined by a harmonizable representation. Under some regularity conditions on Hℓ(tℓ)’s, we establish the result on the modulus of continuity of the sample paths and determine the Hausdorff and packing dimensions of the range B̂H(t)([a,b]) and the graph GrB̂H(t)([a,b]) for [a,b]⊂[ε,T]N, where 0<ε<T<∞, for the multifractional Brownian sheet.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have