Title: Elements of classical theory of stochastic processes
Abstract: This chapter contains a general notion of random processes with continuous time. It is given in context of the Kolmogorov consistency theorem. The notion of a Wiener process with variety of its properties are also presented here. Its existence is stated by two ways: with the help of the Kolmogorov theorem as well as with the help of orthogonal functional systems. Besides the Wiener process as a basic process for many others, the Poisson process is also considered here. Stochastic integration with respect to Wiener process is developed for a class of progressively measurable functions. It leads to the Ito processes, the Ito formula, the Girsanov theorem and representation of martingales (see [5], [6], [14], [17], [21], [35], [41], and [44]).
Publication Year: 2023
Publication Date: 2023-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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