Degenerate Dirichlet Problems Related to the Invariant Measure of Elasto-Plastic Oscillators

Degenerate Dirichlet Problems Related to the Invariant Measure of Elasto-Plastic Oscillators A stochastic variational inequality is proposed to model a white noise excited elasto-plastic oscillator. The solution of this inequality is essentially a continuous diffusion process for which a governing diffusion equation is obtained to study the evolution in time of its probability distribution. The diffusion equation is degenerate, but using the fact that the degeneracy occurs on a bounded region we are able to show the existence of a unique solution satisfying the desired properties. We prove the ergodic properties of the process and characterize the invariant measure. Our approach relies on extending Khasminskii’s method (Stochastic Stability of Differential Equations, Sijthoff and Noordhoff, 1980 ), which in the present context leads to the study of degenerate Dirichlet problems with nonlocal boundary conditions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Degenerate Dirichlet Problems Related to the Invariant Measure of Elasto-Plastic Oscillators

Loading next page...
 
/lp/springer_journal/degenerate-dirichlet-problems-related-to-the-invariant-measure-of-dJ8nyt14VZ
Publisher
Springer-Verlag
Copyright
Copyright © 2008 by Springer Science+Business Media, LLC
Subject
Mathematics; Numerical and Computational Methods ; Mathematical Methods in Physics; Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-007-9027-4
Publisher site
See Article on Publisher Site

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches

$49/month

Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588

$360/year

billed annually
Start Free Trial

14-day Free Trial