Aging scaled Brownian motion.

Heavy Traffic Limits via Brownian Embeddings

For the GI0GI01 queue we show that the scaled queue size converges to reflected Brownian motion in a critical queue and converges to reflected Brownian motion with drift for a sequence of subcritical queuing models that approach a critical model+ Instead of invoking the topological argument of the usual continuousmapping approach, we give a probabilistic argument using Skorokhod embeddings in B...

Convergence of Scaled Renewal Processes to Fractional Brownian Motion

The superposition process of independent counting renewal processes associated with a heavy-tailed interarrival time distribution is shown to converge weakly after rescaling in time and space to fractional Brownian motion, as the number of renewal processes tends to innnity. Corresponding results for continuous arrival uid processes are discussed.

Branching Brownian Motion: Almost Sure Growth Along Scaled Paths

We give a proof of a result on the growth of the number of particles along chosen paths in a branching Brownian motion. The work follows the approach of classical large deviations results, in which paths in C[0, 1] are rescaled onto C[0, T ] for large T . The methods used are probabilistic and take advantage of modern spine techniques.

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Central Limit Theorem Forthe

The Edwards model in one dimension is a transformed path measure for standard Brownian motion discouraging self-intersections. We prove a central limit theorem for the endpoint of the path, extending a law of large numbers proved by Westwater (1984). The scaled variance is characterized in terms of the largest eigenvalue of a one-parameter family of diierential operators, introduced and analyze...