Buch, Englisch, 172 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 448 g
Buch, Englisch, 172 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 448 g
Reihe: Mathematics and Its Applications
ISBN: 978-0-7923-3213-8
Verlag: Springer Netherlands
U sing stochastic differential equations we can successfully model systems that func tion in the presence of random perturbations. Such systems are among the basic objects of modern control theory. However, the very importance acquired by stochas tic differential equations lies, to a large extent, in the strong connections they have with the equations of mathematical physics. It is well known that problems in math ematical physics involve 'damned dimensions', of ten leading to severe difficulties in solving boundary value problems. A way out is provided by stochastic equations, the solutions of which of ten come about as characteristics. In its simplest form, the method of characteristics is as follows. Consider a system of n ordinary differential equations dX = a(X) dt. (O.l ) Let Xx(t) be the solution of this system satisfying the initial condition Xx(O) = x. For an arbitrary continuously differentiable function u(x) we then have: (0.2) u(Xx(t)) - u(x) = j (a(Xx(t)), ~~ (Xx(t))) dt.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Regelungstechnik
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
Weitere Infos & Material
1. Mean-square approximation of solutions of systems of stochastic differential equations.- 2. Modeling of Itô integrals.- 3. Weak approximation of solutions of systems of stochastic differential equations.- 4. Application of the numerical integration of stochastic equations for the Monte-Carlo computation of Wiener integrals.
