The historical process is constructed to be a superprocess which is enriched so as to contain information on genealogy. This process together with a representation for the associated Palm measures are used to describe the modulus of continuity and equilibrium structure for a cla…
The book develops stochastic integration with respect to "Brownian trees" and its associated stochastic calculus, with the aim of proving pathwise existence and uniqueness in a stochastic equation driven by a historical Brownian motion. We use these results and a Girsanov-type t…
Biology takes a special place among the other natural sciences because biological units, be they pieces of DNA, cells or organisms, reproduce more or less faithfully. As for any other biological processes, reproduction has a large random component. The theory of branching proces…
"Branching processes play an increasingly important role in models of genetics, molecular biology, microbiology, ecology, and evolutionary theory. This book presents this body of mathematical ideas for a biological audience, but should also be enjoyable to mathematicians, if onl…