Chung's law of the iterated logarithm for iterated brownian motion
Cluster continuous time random walks
In a continuous time random walk (CTRW), a random waiting time precedes each random jump. The CTRW model is useful in physics, to model diffusing particles. Its scaling limit is a time-changed process, whose densities solve an anomalous diffusion equation. This paper develops limit theory and governing equations for cluster CTRW, in which a random number of jumps cluster together into a single jump. The clustering introduces a dependence between the waiting times and jumps that significantly affects...
Convergence and convergence rate to fractional Brownian motion for weighted random sums.
Convergence in fractional models and applications.