Optimal relaxed control of stochastic hereditary evolution equations with Lévy noise
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In: Control, optimisation and calculus of variations, Vol. 25.2019, No. 48, 61, 25.10.2019.
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TY - JOUR
T1 - Optimal relaxed control of stochastic hereditary evolution equations with Lévy noise
AU - Manna, Utpal
AU - Mukherjee, Debopriya
PY - 2019/10/25
Y1 - 2019/10/25
N2 - Existence theory of optimal relaxed control problem for a class of stochastic hereditary evolution equations driven by Lévy noise has been studied. We formulate the problem in the martingale sense of Stroock and Varadhan to establish existence of optimal controls. The construction of the solution is based on the classical Faedo-Galerkin approximation, the compactness method and the Jakubowski version of the Skorokhod theorem for nonmetric spaces, and certain compactness properties of the class of Young measures on Suslin metrizable control sets. As application of the abstract theory, Oldroyd and Jeffreys fluids have been studied and existence of optimal relaxed control is established. Existence and uniqueness of a strong solution and uniqueness in law for the two-dimensional Oldroyd and Jeffreys fluids are also shown.
AB - Existence theory of optimal relaxed control problem for a class of stochastic hereditary evolution equations driven by Lévy noise has been studied. We formulate the problem in the martingale sense of Stroock and Varadhan to establish existence of optimal controls. The construction of the solution is based on the classical Faedo-Galerkin approximation, the compactness method and the Jakubowski version of the Skorokhod theorem for nonmetric spaces, and certain compactness properties of the class of Young measures on Suslin metrizable control sets. As application of the abstract theory, Oldroyd and Jeffreys fluids have been studied and existence of optimal relaxed control is established. Existence and uniqueness of a strong solution and uniqueness in law for the two-dimensional Oldroyd and Jeffreys fluids are also shown.
KW - Hereditary evolution equations
KW - Jeffreys fluid
KW - Martingale solution
KW - Oldroyd fluid
KW - Relaxed controls
KW - Young measure
UR - http://www.scopus.com/inward/record.url?scp=85074449846&partnerID=8YFLogxK
U2 - 10.1051/cocv/2018066
DO - 10.1051/cocv/2018066
M3 - Article
AN - SCOPUS:85074449846
VL - 25.2019
JO - Control, optimisation and calculus of variations
JF - Control, optimisation and calculus of variations
SN - 1292-8119
IS - 48
M1 - 61
ER -
