On differential equations and inclusions with mean derivatives on a compact manifold

S.V. Azarina; Yu.E. Gliklikh

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2007)

  • Volume: 27, Issue: 2, page 385-397
  • ISSN: 1509-9407

Abstract

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We introduce and investigate a new sort of stochastic differential inclusions on manifolds, given in terms of mean derivatives of a stochastic process, introduced by Nelson for the needs of the so called stochastic mechanics. This class of stochastic inclusions is ideologically the closest one to ordinary differential inclusions. For inclusions with forward mean derivatives on manifolds we prove some results on the existence of solutions.

How to cite

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S.V. Azarina, and Yu.E. Gliklikh. "On differential equations and inclusions with mean derivatives on a compact manifold." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 27.2 (2007): 385-397. <http://eudml.org/doc/271188>.

@article{S2007,
abstract = {We introduce and investigate a new sort of stochastic differential inclusions on manifolds, given in terms of mean derivatives of a stochastic process, introduced by Nelson for the needs of the so called stochastic mechanics. This class of stochastic inclusions is ideologically the closest one to ordinary differential inclusions. For inclusions with forward mean derivatives on manifolds we prove some results on the existence of solutions.},
author = {S.V. Azarina, Yu.E. Gliklikh},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {mean derivatives; differential inclusions; stochastic processes on manifolds; stochastic process},
language = {eng},
number = {2},
pages = {385-397},
title = {On differential equations and inclusions with mean derivatives on a compact manifold},
url = {http://eudml.org/doc/271188},
volume = {27},
year = {2007},
}

TY - JOUR
AU - S.V. Azarina
AU - Yu.E. Gliklikh
TI - On differential equations and inclusions with mean derivatives on a compact manifold
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2007
VL - 27
IS - 2
SP - 385
EP - 397
AB - We introduce and investigate a new sort of stochastic differential inclusions on manifolds, given in terms of mean derivatives of a stochastic process, introduced by Nelson for the needs of the so called stochastic mechanics. This class of stochastic inclusions is ideologically the closest one to ordinary differential inclusions. For inclusions with forward mean derivatives on manifolds we prove some results on the existence of solutions.
LA - eng
KW - mean derivatives; differential inclusions; stochastic processes on manifolds; stochastic process
UR - http://eudml.org/doc/271188
ER -

References

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