Publication Cover
Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 9
45
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Solvability of Langevin differential inclusions with set-valued diffusion terms on Riemannian manifolds

, &
Pages 1105-1116 | Received 19 Mar 2007, Accepted 04 Jul 2007, Published online: 04 Oct 2007

References

  • Aubin , J-P and Cellina , A . 1984 . Differential Inclusions. Set-valued Maps and Viability Theory , Berlin : Springer-Verlag .
  • Billingsley , P . 1969 . Convergence of Probability Measures , New York : Wiley .
  • Bishop , RL and Crittenden , RJ . 1964 . Geometry of Manifolds , New York, London : Springer-Verlag .
  • Borisovich , YG , Gel'man , BD , Myshkis , AD and Obukhovskiĭ , VV . 2005 . Introduction to the Theory of Set-valued Mappings and Differential Inclusions , Moscow : KomKniga . (In Russian)
  • Elworthy , KD . 2005 . “ Stochastic differential equations on manifolds ” . In Notes of London Math. Soc. , Vol. 70 , Cambridge : Cambridge University Press .
  • Gel'man , BD . 2005 . Continuous approximations of set-valued masppings and fixed points . Mathematical Notices , 78 ( 2 ) : 212 – 222 .
  • Gihman , II and Skorohod , AV . 1974 . Theory of Stochastic Processes , Vol. 1 , New York : Springer-Verlag .
  • Gihman , II and Skorohod , AV . 1979 . Theory of Stochastic Processes , Vol. 3 , New York : Springer-Verlag .
  • Gliklikh , YE and Fedorenko , IV . 1980 . On the geometrization of a certain class of mechanical systems with random perturbations of the force. Voronezh University , Deposited in VINITI. October 21, N 4481 (In Russian)
  • Gliklikh , YE and Fedorenko , IV . 1981 . “ Equations of geometric mechanics with random force fields ” . In Priblizhennye metody issledovaniya differentsial'nykh uravneniĭ i ikh prilozheniya , 64 – 72 . Kuĭbyshev . (In Russian)
  • Gliklikh , YE . 1984 . “ Riemannian Parallel Translation in Non-linear Mechanics ” . In Lecture Notes in Mathematics , Vol. 1108 , 128 – 151 . New York : Springer-Verlag .
  • Gliklikh , YE . 1997 . Global Analysis in Mathematical Physics. Geometric and Stochastic Methods , New York : Springer-Verlag .
  • Gliklikh , YE and Obukhovskii , AV . 2001 . Stochastic differential inclusions of Langevin type on Riemannian manifolds . Discussiones Mathematicae. Differential Inclusions, Control and Optimization , 21 ( 2 ) : 173 – 190 .
  • Gliklikh , YE . 2005 . Stochastic and global analysis in problems of mathematical physics , Moscow : KomKniga . (URSS) (In Russian)
  • Kolmogorov , AN and Fomin , SV . 1968 . Elements of Theory of Functions and Functional Analysis , Moscow : Nauka .
  • Leandre , R and Mohammed , SEA . 2001 . Stochastic functional differential equations on Manifolds . Probability Theory and Related Fields , 121 ( 1 ) : 117 – 135 .
  • Meyer , PA . 1981 . “ A Differential Geometric Formalism for the Ito Calculus ” . In Lecture Notes in Mathematics , Vol. 851 , 256 – 270 . New York : Springer-Verlag .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.