RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Journal history

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Fundam. Prikl. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Fundam. Prikl. Mat., 2016, Volume 21, Issue 4, Pages 67–98 (Mi fpm1748)  

The Wiener measure on the Heisenberg group and parabolic equations

S. V. Mamon

Lomonosov Moscow State University

Abstract: In this paper, we study questions related to the theory of stochastic processes on Lie nilpotent groups. In particular, we consider the stochastic process on the Heisenberg group $H_3(\mathbb{R})$ whose trajectories satisfy the horizontal conditions in the stochastic sense relative to the standard contact structure on $H_3(\mathbb{R})$. It is shown that this process is a homogeneous Markov process relative to the Heisenberg group operation. There was found a representation in the form of a Wiener integral for a one-parameter linear semigroup of operators for which the Heisenberg sublaplacian generated by basis vector fields of the corresponding Lie algebra $L(H_3)$ is producing. The main method of solving the problem in this paper is using the path integrals technique, which indicates the common direction of further development of the results.

Full text: PDF file (310 kB)
References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
UDC: 512.813.52+517.955.4+517.983.37+517.987.4+519.216.22

Citation: S. V. Mamon, “The Wiener measure on the Heisenberg group and parabolic equations”, Fundam. Prikl. Mat., 21:4 (2016), 67–98

Citation in format AMSBIB
\Bibitem{Mam16}
\by S.~V.~Mamon
\paper The Wiener measure on the Heisenberg group and parabolic equations
\jour Fundam. Prikl. Mat.
\yr 2016
\vol 21
\issue 4
\pages 67--98
\mathnet{http://mi.mathnet.ru/fpm1748}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3783797}


Linking options:
  • http://mi.mathnet.ru/eng/fpm1748
  • http://mi.mathnet.ru/eng/fpm/v21/i4/p67

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Фундаментальная и прикладная математика
    Number of views:
    This page:56
    Full text:17
    References:4

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019