scholarly journals Second order limit laws for the local times of stable processes

1991 ◽  
pp. 407-424 ◽  
Author(s):  
Jay Rosen
Keyword(s):  
Second Order ◽  
Local Times ◽  
Stable Processes ◽  
Limit Laws

scholarly journals Second-order limit laws for occupation times of fractional Brownian motion

2017 ◽  
Vol 54 (2) ◽  
pp. 444-461 ◽  
Author(s):  
Fangjun Xu
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Method Of Moments ◽  
Second Order ◽  
Hurst Index ◽  
Occupation Times ◽  
Limit Laws ◽  
Additive Functionals ◽  
Finite Dimensional ◽  
Functional Version

Abstract We prove a second-order limit law for additive functionals of a d-dimensional fractional Brownian motion with Hurst index H = 1 / d, using the method of moments and extending the Kallianpur–Robbins law, and then give a functional version of this result. That is, we generalize it to the convergence of the finite-dimensional distributions for corresponding stochastic processes.

From additive to second-order processes

2021 ◽  
pp. 205-215
Author(s):  
M. Rao ◽  
R. Swift
Keyword(s):  
Stochastic Processes ◽  
Poisson Process ◽  
Broad Class ◽  
Second Order ◽  
Stable Processes ◽  
Natural Evolution ◽  
Random Measures ◽  
Additive Processes ◽  
Harmonizable Processes ◽  
Birth Death

The familiar Poisson process is a member of a class of stochastic processes known as additive processes. This broad class also contains the birth-death processes. Second-order processes are processes with two moments finite. The class of second-order processes includes the well-known weakly stationary as well as harmonizable processes. A natural evolution of concepts linking the class of additive processes and the class of second-order processes will be detailed. The connection arises via stable processes and random measures

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