A class of asymptotically self-similar stable processes with stationary increments

作者：Can Sami Umut^*

来源：Stochastic Processes and Their Applications, 2014, 124(12): 3986-4011.

DOI：10.1016/j.spa.2014.07.014

• Stable process
• Self-similar process
• Continuous additive functional
• Local time
• Random walk

We generalize the BM-local time fractional symmetric alpha-stable motion introduced in Cohen and Samorodnitsky (2006) by replacing the local time with a general continuous additive functional (CAF). We show that the resulting process is again symmetric alpha-stable with stationary increments. Depending on the CAF, the process is either self-similar or lies in the domain of attraction of the BM-local time fractional symmetric alpha-stable motion. We also show that the process arises as a weak limit of a discrete "random rewards scheme" similar to the one described by Cohen and Samorodnitsky.

• 出版日期2014-12