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...
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 <∑
...
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
...
Download Results (CSV)