Combining losing games into a winning game

Parrondo's paradox is extended to regime switching random walks in random environments. The paradoxical behavior of the resulting random walk is explained by the effect of the random environment. Full characterization of the asymptotic behavior is achieved in terms of the dimensions of some random subspaces occurring in Oseledec's theorem. The regime switching mechanism gives our models a richer and more complex asymptotic behavior than the simple random walks in random environments appearing in the literature, in terms of transience and recurrence

On the scaling theorem for interacting Fleming-Viot processes

AbstractWe prove an extended version of the scaling theorem for interacting Fleming—Viot processes, in the sense of weak convergence for stochastic processes

Tanaka formula and local time for a class of interacting branching measure-valued diffusions

We construct superprocesses with dependent spatial motion (SDSMs) in Euclidean spaces and show that, even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on $\R^d$, their local times exist when $d\le3$. A Tanaka formula is also derived