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Some optimal control problems for partial differential inclusions [PDF]
Opuscula Mathematica, 2008 Partial differential inclusions are considered. In particular, basing on diffusions properties of weak solutions to stochastic differential inclusions, some existence theorems and some properties of solutions to partial differential inclusions are given.
Michał Kisielewicz
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Discrete Dynamics in Nature and Society, 2018 Linear feedback control and adaptive feedback control are proposed to achieve the synchronization of stochastic neutral-type memristive neural networks with mixed time-varying delays.
Desheng Hong +2 more
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Dynamics of economic growth: Uncertainty treatment using differential inclusions
MethodsX, 2019 The article is focused on applications of the differential inclusions to the models of economic growth, rather than the model building. The models are taken from the known literature, and some modifications are introduced to reflect an additional inertia.
Stanislaw Raczynski
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Existence of weak solutions to stochastic evolution inclusions [PDF]
, 2004 We consider the Cauchy problem for a semilinear stochastic differential inclusion in a Hilbert space. The linear operator generates a strongly continuous semigroup and the nonlinear term is multivalued and satisfies a condition which is more heneral than
De Fitte, Paul Raynaud +2 more
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Localized bases for finite dimensional homogenization approximations with non-separated scales and high-contrast [PDF]
, 2010 We construct finite-dimensional approximations of solution spaces of divergence form operators with $L^\infty$-coefficients. Our method does not rely on concepts of ergodicity or scale-separation, but on the property that the solution space of these ...
Owhadi, Houman, Zhang, Lei
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Optimal solutions to stochastic differential inclusions [PDF]
Applicationes Mathematicae, 2002 The main aim of this paper is to establish an existence theorem for the optimal weak solution \(\xi^{\ast}\) of the following problem: \[ \begin{split} E \int_{0}^{T} h(t,\xi^{\ast}_{t} ) \, dt & = \sup_{\xi} E \int_{0}^{T} h(t, \xi_{t} ) \, dt \\ \text{s.t.} \quad d\xi_{t} & \in F(t,\xi_{t} ) \, dt + G(t, \xi_{t} ) \, dW_{t} \\ P^{\xi_{0}}& = \mu ...
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A market model: uncertainty and reachable sets
International Journal for Simulation and Multidisciplinary Design Optimization, 2015 Uncertain parameters are always present in models that include human factor. In marketing the uncertain consumer behavior makes it difficult to predict the future events and elaborate good marketing strategies.
Raczynski Stanislaw
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On the Solution of Stochastic Differential Inclusion
Journal of Mathematical Analysis and Applications, 1995 Let \((\Omega, \Lambda,p)\) be a probability space, \(I = [0,T]\), \(\{\Lambda_t \}_{t \in I}\) an increasing family of \(\sigma\)- subalgebras such that \(\bigcap_{\alpha > 0} \Lambda _{t + \alpha} = \Lambda_t\), and \(\beta_t\) a \(\sigma\)-algebra of all Borel subsets of \([0,t]\) for fixed \(t \in I\). Let us denote by \(\beta \Lambda\) a \(\sigma\)
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On Stochastic Differential Inclusions with Current Velocities
Journal of Computational and Engineering Mathematics, 2015 Existence of solution theorems are obtained for stochastic differential inclusions given in terms of the so-called current velocities (symmetric mean derivatives, a direct analogs of ordinary velocity of deterministic systems) and quadratic mean derivatives (giving information on the diffusion coefficient) on the flat $n$-dimensional torus.
Yu.E. Gliklikh, A.V. Makarova
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Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2017 Notion of mean derivatives was introduced by Edward Nelson for the needs of stochastic mechanics (a version of quantum mechanics). Nelson introduced forward and backward mean derivatives while only their half-sum, symmetric mean derivative called current
Alla V Makarova +2 more
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