Overview
I have a particular interest in the evolution of random processes over time. Examples include: the evolution of soil moisture in response to steady evaporation and drainage and random shocks of precipitation; the evolution of small sandy islands as they are eroded by currents some of the time but accumulate sand or silt carried onto it by currents at other times; the transmission of infectious diseases through a community or of memes through a social network; the drift of a buoy in the ocean, stock prices in a market, or your rating in an e-sport on the online competitive ladder.
What these have in common is that the interesting behavior isn't in the average path—it's in the variability around it, the persistence of shocks, and the probability of ending up somewhere extreme. Systems like these are frequently modeled with a deterministic trend plus noise treated as an afterthought, which systematically understates how often the process visits the states you actually care about.
Related Work
Much of my applied work in flood risk depends directly on this. Antecedent soil moisture is a stochastic process, and the worst floods often occur when a storm arrives on ground that a previous storm already saturated—a dependency that models assuming average soil moisture conditions cannot represent. I've also got a methods paper pending on a way to cut compute costs by 10–30x when running computationally expensive simulations of random inputs under adequate smoothness conditions.
Further Reading
- A stochastic treatment of soil moisture dynamics. Water Resources Research, 2025.