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Graduate Course - J.A. Goldstein - 2019

Graduate Course on
Semigroups in Mathematical Finance and Quantum Mechanical Scattering Theory
Jerry Goldstein, Bari, 2019
 
The course consists of four lectures, each one lasting for two hours.
Lecture #1. Remarks on Brownian motion and stochastic differential equations. The Nobel Prize winning Black-Merton-Scholes equation for stock options. The governing semigroup: explicit representation formula and the chaos property.
Lecture #2. The Cox-Ingersoll-Ross bond equation. We survey the current theory, which is changing rapidly. This includes construction of the semigroup, the unexpected boundary conditions, a new type of Feynman-Kac formula, plus other topics.
Lecture #3. Introduction to classical mechanics and quantum mechanics. Examples in quantum mechanics, involving bound states (eigenfunctions).
Lecture #4.  Quantum mechanical scattering theory. Perturbation of continuous spectra. Remarks on inverse problems.
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