Skip to main content

Interactive Drifts

  • 1669 Accesses

Part of the Lecture Notes in Mathematics book series (LNMECOLE,volume 1781)

Abstract

Our objective is to study measure-valued diffusions which locally behave like DW-superprocesses, much in the same way as solutions to Ito–s stochastic differential equations behave locally like Brownian motions. This means that we want to consider processes in which the branching rate, γ, the spatial generator, A, and the drift, g, all depend on the current state of the system, Xt, or more generally on the past behaviour of the system, X|[0,t]. One suspects that these dependencies are listed roughly in decreasing order of difficulty. In this Chapter we present a general result of Dawson which, for a large class of interactive drifts, will give an explicit formula for the Radon-Nikodym derivative of law of the interactive model with respect to that of a driftless DW-superprocess.

Keywords

  • Martingale Measure
  • Local Martingale
  • Martingale Problem
  • Continuous Local Martingale
  • Branch Particle System

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

(2002). Interactive Drifts. In: Bernard, P. (eds) Lectures on Probability Theory and Statistics. Lecture Notes in Mathematics, vol 1781. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47944-9_8

Download citation

  • DOI: https://doi.org/10.1007/3-540-47944-9_8

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43736-9

  • Online ISBN: 978-3-540-47944-4

  • eBook Packages: Springer Book Archive