Skip to main content

The Case of General Symmetric Markov Processes

  • 1163 Accesses

Part of the Lecture Notes in Mathematics book series (LNMECOLE,volume 2026)

Abstract

We now explain briefly how some of the above results can be extended to symmetric Markov processes on continuous spaces. The construction of the loop measure as well as a lot of computations can be performed quite generally, using Markov processes or Dirichlet space theory (Cf. for example [10]). \(\mathbb{P}_\text{t} ^{x,y}\)can be properly defined. The semigroup should have a density with respect to the duality measure given by a locally integrable kernel pt(x, y). This is very often the case in examples of interest, especially in finite dimensional spaces.

Keywords

  • Brownian Motion
  • Green Function
  • Trace Class
  • Hilbert Schmidt Operator
  • Capacitary Measure

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   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   49.95
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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yves Le Jan .

Rights and permissions

Reprints and Permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Jan, Y.L. (2011). The Case of General Symmetric Markov Processes. In: Markov Paths, Loops and Fields. Lecture Notes in Mathematics(), vol 2026. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21216-1_10

Download citation