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- Agram, Nacira, et al.
(författare)
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Singular Control Of Stochastic Volterra Integral Equations
- 2022
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Ingår i: Acta Mathematica Scientia. - : Springer Nature. - 0252-9602 .- 1003-3998 .- 1572-9087. ; 42:3, s. 1003-1017
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Tidskriftsartikel (refereegranskat)abstract
- This paper deals with optimal combined singular and regular controls for stochastic Volterra integral equations, where the solution X-u,X-xi(t) =X(t) is given by X(t) = phi(t) + integral(t)(0) b (t, s, X(s), u(s)) ds + integral(t)(0) sigma (t, s, X(s), u(s)) dB(s) + integral(t )(0)h (t, s) d xi(s). Here dB(s) denotes the Brownian motion Ito type differential, xi denotes the singular control (singular in time t with respect to Lebesgue measure) and u denotes the regular control (absolutely continuous with respect to Lebesgue measure). Such systems may for example be used to model harvesting of populations with memory, where X(t) represents the population density at time t, and the singular control process xi represents the harvesting effort rate. The total income from the harvesting is represented by J(u, xi) = E[integral(T)(0) f(0)(t, X(t), u(t))dt + integral(T)(0) f(1)(t, X(t))d xi(t) + g(X(T))], for the given functions f(0), f(1) and g, where T > 0 is a constant denoting the terminal time of the harvesting. Note that it is important to allow the controls to be singular, because in some cases the optimal controls are of this type. Using Hida-Malliavin calculus, we prove sufficient conditions and necessary conditions of optimality of controls. As a consequence, we obtain a new type of backward stochastic Volterra integral equations with singular drift. Finally, to illustrate our results, we apply them to discuss optimal harvesting problems with possibly density dependent prices.
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| 2. |
- de Gosson, Maurice, et al.
(författare)
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Continuity Properties for Born-Jordan Operators with Symbols in Hörmander Classes and Modulation Spaces
- 2020
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Ingår i: Acta Mathematica Scientia. - : Springer. - 0252-9602 .- 1003-3998 .- 1572-9087. ; 40:6, s. 1603-1626
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Tidskriftsartikel (refereegranskat)abstract
- We show that the Weyl symbol of a Born-Jordan operator is in the same class as the Born-Jordan symbol, when Hormander symbols and certain types of modulation spaces are used as symbol classes. We use these properties to carry over continuity, nuclearity and Schatten-von Neumann properties to the Born-Jordan calculus.
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| 3. |
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| 4. |
- Tephnadze, George
(författare)
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Approximation by walsh-kaczmarz-fejér means on the hardy space
- 2014
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Ingår i: Acta Mathematica Scientia. - 0252-9602 .- 1003-3998. ; 34:5, s. 1593-1602
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Tidskriftsartikel (refereegranskat)abstract
- The main aim of this paper is to find necessary and sufficient conditions for the convergence of Walsh-Kaczmarz-Fejér means in the terms of the modulus of continuity on the Hardy spaces Hp, when 0
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| 6. |
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| 7. |
- Dam, Hai Huyen, et al.
(författare)
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Spreading Code Design Using a Global Optimization Method
- 2005
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Ingår i: Annals of Operations Research. - : Springer. - 0254-5330 .- 1572-9338. ; 133:1-4, s. 249-264
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Tidskriftsartikel (refereegranskat)abstract
- The performance of a code division multiple access system depends on the correlation properties of the employed spreading code. Low cross-correlation values between spreading sequences are desired to suppress multiple access interference and to improve bit error performance. An auto-correlation function with a distinct peak enables proper synchronization and suppresses intersymbol interference. However, these requirements contradict each other and a trade-off needs to be established. In this paper, a global two dimensional optimization method is proposed to minimize the out-of-phase average mean-square aperiodic auto-correlation with average mean-square aperiodic cross-correlation being allowed to lie within a fixed region. This approach is applied to design sets of complex spreading sequences. A design example is presented to illustrate the relation between various correlation characteristics. The correlations of the obtained sets are compared with correlations of other known sequences.
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