On mild solutions of gradient systems in Hilbert spaces

Andrzej Rozkosz

Open Mathematics (2013)

  • Volume: 11, Issue: 11, page 1994-2004
  • ISSN: 2391-5455

Abstract

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We consider the Cauchy problem for an infinite-dimensional Ornstein-Uhlenbeck equation perturbed by gradient of a potential. We prove some results on existence and uniqueness of mild solutions of the problem. We also provide stochastic representation of mild solutions in terms of linear backward stochastic differential equations determined by the Ornstein-Uhlenbeck operator and the potential.

How to cite

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Andrzej Rozkosz. "On mild solutions of gradient systems in Hilbert spaces." Open Mathematics 11.11 (2013): 1994-2004. <http://eudml.org/doc/269307>.

@article{AndrzejRozkosz2013,
abstract = {We consider the Cauchy problem for an infinite-dimensional Ornstein-Uhlenbeck equation perturbed by gradient of a potential. We prove some results on existence and uniqueness of mild solutions of the problem. We also provide stochastic representation of mild solutions in terms of linear backward stochastic differential equations determined by the Ornstein-Uhlenbeck operator and the potential.},
author = {Andrzej Rozkosz},
journal = {Open Mathematics},
keywords = {Gradient systems; Ornstein-Uhlenbeck operator; Mild solution; Backward stochastic differential equation; gradient systems; mild solution; backward stochastic differential equation},
language = {eng},
number = {11},
pages = {1994-2004},
title = {On mild solutions of gradient systems in Hilbert spaces},
url = {http://eudml.org/doc/269307},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Andrzej Rozkosz
TI - On mild solutions of gradient systems in Hilbert spaces
JO - Open Mathematics
PY - 2013
VL - 11
IS - 11
SP - 1994
EP - 2004
AB - We consider the Cauchy problem for an infinite-dimensional Ornstein-Uhlenbeck equation perturbed by gradient of a potential. We prove some results on existence and uniqueness of mild solutions of the problem. We also provide stochastic representation of mild solutions in terms of linear backward stochastic differential equations determined by the Ornstein-Uhlenbeck operator and the potential.
LA - eng
KW - Gradient systems; Ornstein-Uhlenbeck operator; Mild solution; Backward stochastic differential equation; gradient systems; mild solution; backward stochastic differential equation
UR - http://eudml.org/doc/269307
ER -

References

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  8. [8] Fuhrman M., Tessitore G., Nonlinear Kolmogorov equations in infinite dimensional spaces: the backward stochastic differential equations approach and applications to optimal control, Ann. Probab., 2002, 30(3), 1397–1465 http://dx.doi.org/10.1214/aop/1029867132 Zbl1017.60076
  9. [9] Oharu S., Takahashi T., Characterization of nonlinear semigroups associated with semilinear evolution equations, Trans. Amer. Math. Soc., 1989, 311(2), 593–619 http://dx.doi.org/10.1090/S0002-9947-1989-0978369-9 Zbl0679.58011

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