Exponential Integrability and Application to Stochastic Quantization

Exponential Integrability and Application to Stochastic Quantization Appl Math Optim 37:295–353 (1998) 1998 Springer-Verlag New York Inc. Exponential Integrability and Application to Stochastic Quantization ¤¤ Y. Hu and G. Kallianpur Center for Stochastic Processes, Department of Statistics, The University of North Carolina at Chapel Hill, 321 Phillips Hall, Chapel Hill, NC 27599-3260, USA Abstract. We study the exponential integrability problem for I . f /, i.e., n n E expf I . f /g < 1, where I . f / is a multiple Ito–W ˆ iener integral on some Gaus- n n n n sian space arising from the constructive quantum field theory and from stochastic quantization. We also study a class of singular infinite-dimensional stochastic dif- ferential equations whose drift coefficients are measurable and unbounded. Using a condition due to Kazamaki, we prove the existence of a weak solution assuming some integrability conditions on the drift coefficient. Then we apply the exponen- tial integrability theorem and the existence theorem to study infinite-dimensional stochastic differential equations of stochastic quantization. Key Words. P.8/ field, Multiple integral, Stochastic quantization, Infinite- dimensional stochastic differential equation, Exponential integrability, Cameron– Martin–Girsanov theorem. AMS Classification. Primary 60H10, 60H15, Secondary 34F05, 60J60, 60K40, 60G20, 81T08. 1. Introduction Let H be a separable http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Exponential Integrability and Application to Stochastic Quantization

Loading next page...
 
/lp/springer_journal/exponential-integrability-and-application-to-stochastic-quantization-FwV8WxRhWM
Publisher
Springer-Verlag
Copyright
Copyright © Inc. by 1998 Springer-Verlag New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s002459900078
Publisher site
See Article on Publisher Site

There are no references for this article.

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