Faithin Omaha eBook Collection

Download or read book On the Martingale Problem for Interactive Measure-Valued Branching Diffusions written by Edwin Arend Perkins and published by American Mathematical Soc.. This book was released on 1995 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.