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Titre : | STOCHASTIC DIFFERENTIAL EQUATIONS WITH NON-LIPSCHTZIAN COEFFICIENTS |
Auteurs : | F. Benziadi, Directeur de thèse ; Hachemane, Fatima, Auteur |
Type de document : | texte imprimé |
Editeur : | université Dr mouley tahar, Faculté de Science, Saida, Algerie : Alger: univ-saida, 2018 |
ISBN/ISSN/EAN : | SCT01545 |
Format : | 94 p. / 29.5 cm. |
Accompagnement : | + CD |
Note générale : | Biblioghr. |
Langues: | Français |
Catégories : | |
Mots-clés: | STOCHASTIC, DIFFERENTIAL EQUATIONS, NON-LIPSCHTZIAN COEFFICIENTS. |
Résumé : |
In many cases we need to minimize some target functional subject to a controlled dynamical system; for example, to minimize the energy expended by the controlled T system during a period of time, like, minimizing E 0x ut
|x ut | 2 dt, where u(·) is a control,is the solution of the system corresponding to the applied control u(·). We will find that the minimal value of the target functional will be obtained when we can apply some extreme solution of the dynamic system. For this example the idea is that at each time when the trajectory of the state process leaves the point 0, we should immediately use a feedback control to fully pull back the trajectory directed towards 0, because if the state x ut is closer to 0, then the energy |x ut | 2 expended is also closer to zero and so it is smaller, even though it cannot be 0. Such an extreme feedback control is called a Bang-Bang control. Obviously, such a feedback control is not Lipschitz continuous, and so it also makes the coefficients of the system non-Lipschitzian, for example, when the system is linear with respect to the control u(·) : the system coefficient is A(t)x t + B(t)u t . However, we need the state of the system, that is, the solution, to exist for such a control, so the system can be controlled. Therefore, discussing solutions for stochastic differential equations (SDEs) with jumps and with non-Lipschitzian coefficients, is necessary and useful from the practical point of view. The interesting thing is also that in the ordinary differential equation (ODE) case, if its coefficients are only continuous then a solution, even when it exists, is not necessary unique. However, in the SDE case we can have a unique solution even when the coefficients are not continuous. This means that a stochastic perturbation can some- times improve the nice properties of the solution. The stochastic integral term is very important in the financial market. Actually, its coefficient corresponds to |
Note de contenu : |
Stochastic calculus
Stochastic differential equations Stochastic differential equations with non-Lipschitzian coefficients |
Exemplaires (1)
Code-barres | Cote | Support | Localisation | Section | Disponibilité |
---|---|---|---|---|---|
SCT01545 | TMMS00345 | Périodique | Salle des Thèses | Mathématique | Exclu du prêt |
Documents numériques (1)
![]() ![]() STOCHASTIC DIFFERENTIAL EQUATIONS WITH NON-LIPSCHTZIAN COEFFICIENTS Adobe Acrobat PDF |