Sectorial local non-determinism and the geometry of the Brownian sheet.
α-time fractional brownian motion: PDE connections and local times
For 0 < ≤ 2 and 0 < < 1, an -time fractional Brownian motion is an iterated process = {() = (()) ≥ 0} obtained by taking a fractional Brownian motion {() ∈ ℝ} with Hurst index 0 < < 1 and replacing the time parameter with a strictly -stable Lévy process {() ≥ 0} in ℝ independent of {() ∈ R}. It is shown that such processes have natural connections to partial differential equations and, when is a stable subordinator, can arise as scaling limit of randomly...
Joint continuity of the local times of fractional brownian sheets
Let ={ (), ∈ℝ } be an (, )-fractional brownian sheet with index =( , …, )∈(0, 1) defined by ()=( (), …, ()) (∈ℝ ), where , …, are independent copies of a real-valued fractional brownian sheet . We prove that if <∑ ...
α-time fractional Brownian motion: PDE connections and local times
For 0 < ≤ 2 and 0 < < 1, an -time fractional Brownian motion is an iterated process = {() = (()) ≥ 0} obtained by taking a fractional Brownian motion {() ∈ ℝ} with Hurst index 0 < < 1 and replacing the time parameter with a strictly -stable Lévy process {() ≥ 0} in ℝ independent of {() ∈ R}. It is shown that such processes have natural connections to partial differential equations and, when ...
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