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    Wyświetlanie 1-10 z 10
    Tytuł:
    Existence of solutions for second order stochastic differential inclusions in Hilbert spaces
    Autorzy:
    Balasubramaniam, P.
    Ntouyas, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/729455.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    existence
    multivalued map
    stochastic differential inclusions
    fixed point
    Hilbert space
    Opis:
    In this paper, sufficient conditions are given for the existence of solutions for a class of second order stochastic differential inclusions in Hilbert space with the help of Leray-Schauder Nonlinear Alternative.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 365-384
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A relaxation theorem for partially observed stochastic control on Hilbert space
    Autorzy:
    Ahmed, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/729417.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    partially observed control
    infinite dimensional Hilbert space
    relaxed controls
    Zakai equation
    Opis:
    In this paper, we present a result on relaxability of partially observed control problems for infinite dimensional stochastic systems in a Hilbert space. This is motivated by the fact that measure valued controls, also known as relaxed controls, are difficult to construct practically and so one must inquire if it is possible to approximate the solutions corresponding to measure valued controls by those corresponding to ordinary controls. Our main result is the relaxation theorem which states that the set of solutions corresponding to ordinary controls is weakly dense in the set of solutions corresponding to relaxed controls. This is presented in Theorem 5.3 after giving some existence results on optimal controls for the infinite dimensional Zakai equation used for its proof.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 295-314
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A general class of McKean-Vlasov stochastic evolution equations driven by Brownian motion and Lèvy process and controlled by Lèvy measure
    Autorzy:
    Ahmed, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/729570.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    McKean-Vlasov stochastic differential equation
    Hilbert spaces
    existence of optimal controls
    Opis:
    In this paper we consider McKean-Vlasov stochastic evolution equations on Hilbert spaces driven by Brownian motion and L`evy process and controlled by L`evy measures. We prove existence and uniqueness of solutions and regularity properties thereof. We consider weak topology on the space of bounded Le´vy measures on infinite dimensional Hilbert space and prove continuous dependence of solutions with respect to the Le´vy measure. Then considering a certain class of Le´vy measures on infinite as well as finite dimensional Hilbert spaces, as relaxed controls, we prove existence of optimal controls for Bolza problem and some simple mass transport problems
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2016, 36, 2; 181-206
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Stochastic evolution equations on Hilbert spaces with partially observed relaxed controls and their necessary conditions of optimality
    Autorzy:
    Ahmed, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/729524.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    differential equations
    Hilbert spaces
    relaxed controls
    optimal control
    necessary conditions of optimality
    Opis:
    In this paper we consider the question of optimal control for a class of stochastic evolution equations on infinite dimensional Hilbert spaces with controls appearing in both the drift and the diffusion operators. We consider relaxed controls (measure valued random processes) and briefly present some results on the question of existence of mild solutions including their regularity followed by a result on existence of partially observed optimal relaxed controls. Then we develop the necessary conditions of optimality for partially observed relaxed controls. This is the main topic of this paper. Further we present an algorithm for computation of optimal policies followed by a brief discussion on regular versus relaxed controls. The paper is concluded by an example of a non-convex problem which is readily solvable by our approach.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2014, 34, 1; 105-129
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Controllability of evolution equations and inclusions driven by vector measures
    Autorzy:
    Ahmed, N.U.
    Powiązania:
    https://bibliotekanauki.pl/articles/729615.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    controlability
    impulsive systems
    differential inclusions
    Hilbert spaces
    vector valued measures
    C₀ semigroups
    Opis:
    In this paper, we consider the question of controllability of a class of linear and semilinear evolution equations on Hilbert space with measures as controls. We present necessary and sufficient conditions for weak and exact (strong) controllability of a linear system. Using this result we prove that exact controllability of the linear system implies exact controllability of a perturbed semilinear system. Controllability problem for the semilinear system is formulated as a fixed point problem on the space of vector measures and is concluded controllability from the existence of a fixed point. Our results cover impulsive controls as well as regular controls.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2004, 24, 1; 49-72
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Graded Hilbert-symbol equivalence of number fields
    Autorzy:
    Koprowski, Przemysław
    Powiązania:
    https://bibliotekanauki.pl/articles/729195.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Brauer group
    Brauer-Wall group
    Hilbert symbol equivalence
    Witt equivalence
    graded quaternion algebras
    Opis:
    We present a new criterion for the existence of Hilbert-symbol equivalence of two number fields. In principle, we show that the system of local conditions for this equivalence may be expressed in terms of Clifford invariants in place of Hilbert-symbols, shifting the focus from Brauer groups to Brauer-Wall groups.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2015, 35, 1; 105-113
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal control of general McKean-Vlasov stochastic evolution equations on Hilbert spaces and necessary conditions of optimality
    Autorzy:
    Ahmed, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/729626.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    McKean-Vlasov stochastic differential equation
    Hilbert spaces
    relaxed controls
    existence of optimal controls
    Opis:
    In this paper we consider controlled McKean-Vlasov stochastic evolution equations on Hilbert spaces. We prove existence and uniqueness of solutions and regularity properties thereof. We use relaxed controls, adapted to a current of sub-sigma algebras generated by observable processes, and taking values from a Polish space. We introduce an appropriate topology based on weak star convergence. We prove continuous dependence of solutions on controls with respect to appropriate topologies. Theses results are then used to prove existence of optimal controls for Bolza problems. Then we develop the necessary conditions of optimality based on semi-martingale representation theory on Hilbert spaces. Next we show that the adjoint processes arising from the necessary conditions optimality can be constructed from the solution of certain BSDE.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2015, 35, 2; 165-195
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Measure valued solutions for stochastic evolution equations on Hilbert space and their feedback control
    Autorzy:
    Ahmed, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/729584.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    stochastic differential equations
    Hilbert space
    measurable vector fields
    finitely additive measure solutions
    optimal feedback controls
    Opis:
    In this paper, we consider a class of semilinear stochastic evolution equations on Hilbert space driven by a stochastic vector measure. The nonlinear terms are assumed to be merely continuous and bounded on bounded sets. We prove the existence of measure valued solutions generalizing some earlier results of the author. As a corollary, an existence result of a measure solution for a forward Kolmogorov equation with unbounded operator valued coefficients is obtained. The main result is further extended to cover Borel measurable drift and diffusion which are assumed to be bounded on bounded sets. Also we consider control problems for these systems and present several results on the existence of optimal feedback controls.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2005, 25, 1; 129-157
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Topological dual of $B_∞(I, ₁(X,Y))$ with application to stochastic systems on Hilbert space
    Autorzy:
    Ahmed, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/729390.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    representation theory
    topological dual
    finitely additive operator-valued measures
    polish space
    Hilbert space
    stochastic systems
    structural control
    uncertainty abatement
    Opis:
    In this paper, we prove that the topological dual of the Banach space of bounded measurable functions with values in the space of nuclear operators, furnished with the natural topology, is isometrically isomorphic to the space of finitely additive linear operator-valued measures having bounded variation in a Banach space containing the space of bounded linear operators. This is then applied to a stochastic structural control problem. An optimal operator-valued measure, considered as the structural control, is to be chosen so as to minimize fluctuation (volatility). Both existence of optimal policy and necessary conditions of optimality are presented including a conceptual algorithm.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2009, 29, 1; 67-90
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal trend estimation in geometric asset price models
    Autorzy:
    Weba, Michael
    Powiązania:
    https://bibliotekanauki.pl/articles/729704.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    geometric asset price model
    trend estimation
    Wiener process
    Ornstein-Uhlenbeck process
    kernel reproducing Hilbert space
    exogeneous shocks
    compound Poisson process
    Opis:
    In the general geometric asset price model, the asset price P(t) at time t satisfies the relation
    $P(t) = P₀ · e^{α·f(t) + σ·F(t)}$, t ∈ [0,T],
    where f is a deterministic trend function, the stochastic process F describes the random fluctuations of the market, α is the trend coefficient, and σ denotes the volatility.
    The paper examines the problem of optimal trend estimation by utilizing the concept of kernel reproducing Hilbert spaces. It characterizes the class of trend functions with the property that the trend coefficient can be estimated consistently. Furthermore, explicit formulae for the best linear unbiased estimator α̂ of α and representations for the variance of α̂ are derived.
    The results do not require assumptions on finite-dimensional distributions and allow of jump processes as well as exogeneous shocks. .
    Źródło:
    Discussiones Mathematicae Probability and Statistics; 2005, 25, 1; 51-70
    1509-9423
    Pojawia się w:
    Discussiones Mathematicae Probability and Statistics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-10 z 10

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