Let X^H(u)(u)={X^H(u)(u);u∈R^N+}be linear multifractional stable sheets with index functional H(u),where H(u)=(H1(u),…,HN(u))is a function with values in(0;1)N.Based on some assumptions of H(u),we obtain the existen...Let X^H(u)(u)={X^H(u)(u);u∈R^N+}be linear multifractional stable sheets with index functional H(u),where H(u)=(H1(u),…,HN(u))is a function with values in(0;1)N.Based on some assumptions of H(u),we obtain the existence of the local times of X^H(u)(u)and establish its joint continuity and the Holder regularity.These results generalize the corresponding results about fractional stable sheets to multifractional stable sheets.展开更多
Let B^α = {B^α（t）,t E R^N} be an （N,d）-fractional Brownian motion with Hurst index α∈ （0, 1）. By applying the strong local nondeterminism of B^α, we prove certain forms of uniform Hausdorff dimension result...Let B^α = {B^α（t）,t E R^N} be an （N,d）-fractional Brownian motion with Hurst index α∈ （0, 1）. By applying the strong local nondeterminism of B^α, we prove certain forms of uniform Hausdorff dimension results for the images of B^α when N 〉 αd. Our results extend those of Kaufman for one-dimensional Brownian motion.展开更多
文摘Let X^H(u)(u)={X^H(u)(u);u∈R^N+}be linear multifractional stable sheets with index functional H(u),where H(u)=(H1(u),…,HN(u))is a function with values in(0;1)N.Based on some assumptions of H(u),we obtain the existence of the local times of X^H(u)(u)and establish its joint continuity and the Holder regularity.These results generalize the corresponding results about fractional stable sheets to multifractional stable sheets.
基金Research partially supported by NSF Grant DMS-0404729
文摘Let B^α = {B^α（t）,t E R^N} be an （N,d）-fractional Brownian motion with Hurst index α∈ （0, 1）. By applying the strong local nondeterminism of B^α, we prove certain forms of uniform Hausdorff dimension results for the images of B^α when N 〉 αd. Our results extend those of Kaufman for one-dimensional Brownian motion.
