Hunt's hypothesis (H) and Getoor's conjecture for Lévy Processes

Details Hunt's hypothesis (H) and Getoor's conjecture for Lévy Processes Hunt's hypothesis (H) and Getoor's conjecture for Lévy Processes

2011-01-16

arxiv.org/abs/1101.3038v2

Mathematics

Probability

12 pages

Scientific paper

In this paper, Hunt's hypothesis (H) and Getoor's conjecture for L\'{e}vy processes are revisited. Let $X$ be a L\'{e}vy process on $\mathbf{R}^n$ with L\'{e}vy-Khintchine exponent $(a,A,\mu)$. First, we show that if $A$ is non-degenerate then $X$ satisfies (H). Second, under the assumption that $\mu({\mathbf{R}^n\backslash \sqrt{A}\mathbf{R}^n})<\infty$, we show that $X$ satisfies (H) if and only if the equation $$ \sqrt{A}y=-a-\int_{\{x\in {\mathbf{R}^n\backslash \sqrt{A}\mathbf{R}^n}:\,|x|<1\}}x\mu(dx),\ y\in \mathbf{R}^n, $$ has at least one solution. Finally, we show that if $X$ is a subordinator and satisfies (H) then its drift coefficient must be 0.

Affiliated with

Also associated with

No associations

Rating

Hunt's hypothesis (H) and Getoor's conjecture for Lévy Processes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hunt's hypothesis (H) and Getoor's conjecture for Lévy Processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hunt's hypothesis (H) and Getoor's conjecture for Lévy Processes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-626199