5 papers
Occupation Times for Time-changed Processes with Applications to Parisian Options
Joonyong Choi, David Clancy
Stochastic processes time-changed by an inverse subordinator have been suggested as a way to model the price of assets in illiquid markets, where the jumps of the subordinator corr…
Epidemics on critical random graphs with heavy-tailed degree distribution
David Clancy
We study the susceptible-infected-recovered (SIR) epidemic on a random graph chosen uniformly over all graphs with certain critical, heavy-tailed degree distributions. For this mod…
Encoding multitype Galton-Watson forests and a multitype Ray-Knight theorem
David Clancy
We provide a simple forest model to encode the genealogical structure of a multitype Galton-Watson process with immigration. We provide two encodings of these forests by stochastic…
A new relationship between Erdős-Rényi graphs, epidemic models and Brownian motion with parabolic drift
David Clancy
In the Reed-Frost model, an example of an SIR epidemic model, one can examine a statistic that counts the number of concurrently infected individuals. This statistic can be reformu…
The Gorin-Shkolnikov identity and its random tree generalization
David Clancy
In a recent pair of papers Gorin and Shkolnikov (2018) and Hariya (2016) have shown that the area under normalized Brownian excursion minus one half the integral of the square of i…