On the Martingale Problem for Interactive Measure-Valued Branching Diffusions

This 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. Perkins uses these results and a Girsanov-type theorem to prove that the martingale problem for the historical process associated with a wide class of interactive branching measure-valued diffusions (superprocesses) is well-posed. The resulting measure-valued processes will arise as limits of the empirical measures of branching particle systems in which particles interact through their spatial motions or, to a lesser extent, through their branching rates.Perkins, Edwin is the author of 'On the Martingale Problem for Interactive Measure-Valued Branching Diffusions' with ISBN 9780821803585 and ISBN 0821803581.