Читать книгу Numerical Methods in Computational Finance - Daniel J. Duffy - Страница 20

A function that is not continuous at some point is said to be discontinuous at that point. For example, the Heaviside function (1.2) is not continuous at . In order to determine if a function is continuous at a point x in an interval (a, b) we apply the test:

There are two (simple discontinuity) main categories of discontinuous functions:

 First kind: and exists. Then either we have or .

 Second kind: a discontinuity that is not of the first kind.

Examples are:

You can check that this latter function has a discontinuity of the first kind at .