|Author||: Edwin Arend Perkins|
|Publisher||: American Mathematical Soc.|
|Release Date||: 25 September 1995|
|Pages||: 89 pages|
|Rating||: /5 ( users)|
On the Martingale Problem for Interactive Measure Valued Branching Diffusions by Edwin Arend Perkins Book PDF Summary
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.