A transience condition for a class of one-dimensional symmetric Levy processes

作者：Sandric Nikola^*

来源：Electronic Communications in Probability, 2013, 18(0): 1-13.

DOI：10.1214/ecp.v18-2802

• characteristics of a semimartingale
• electrical network
• Levy measure
• Levy process
• random walk
• recurrence
• transience

In this paper, we give a sufficient condition for the transience for a class of one-dimensional symmetric Levy processes. More precisely, we prove that a one-dimensional symmetric Levy process with the Levy measure nu(dy) = f(y) dy or nu({n} g) = p(n), where the density function f(y) is such that f(y) %26gt; 0 a.e. and the sequence {p(n)}(n %26gt;= 1) is such that p(n) %26gt; 0 for all n %26gt;= 1, is transient if %26lt;br%26gt;integral(infinity)(1) dy/y(3)f(y) %26lt; infinity or Sigma(infinity)(n=1) 1/n(3)p(n) %26lt; infinity. %26lt;br%26gt;Similarly, we derive an analogous transience condition for one-dimensional symmetric random walks with continuous and discrete jumps.

• 出版日期2013-8-24