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On the Martingale Problem for Interactive Measure-Valued Branching Diffusions
 
On the Martingale Problem for Interactive Measure-Valued Branching Diffusions
eBook ISBN:  978-1-4704-0128-3
Product Code:  MEMO/115/549.E
List Price: $41.00
MAA Member Price: $36.90
AMS Member Price: $24.60
On the Martingale Problem for Interactive Measure-Valued Branching Diffusions
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On the Martingale Problem for Interactive Measure-Valued Branching Diffusions
eBook ISBN:  978-1-4704-0128-3
Product Code:  MEMO/115/549.E
List Price: $41.00
MAA Member Price: $36.90
AMS Member Price: $24.60
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1151995; 89 pp
    MSC: Primary 60;

    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.

    Readership

    Research mathematicians.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Historical integrals and stochastic calculus
    • 3. On the compact support property
    • 4. Pathwise existence and uniqueness in a stochastic equation for historical processes
    • 5. Existence and uniqueness for a historical martingale problem
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1151995; 89 pp
MSC: Primary 60;

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.

Readership

Research mathematicians.

  • Chapters
  • 1. Introduction
  • 2. Historical integrals and stochastic calculus
  • 3. On the compact support property
  • 4. Pathwise existence and uniqueness in a stochastic equation for historical processes
  • 5. Existence and uniqueness for a historical martingale problem
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.