Section 19.1 introduces the fundamental concept of infinitely divisible distributions and contains the key theorem on relationship of such processes to processes with independent homogeneous increments. Section 19.2 begins with a definition of the Wiener process based on its finite-dimensional distributions and establishes existence of a continuous modification of the process. It also derives the distribution of the maximum of the Wiener process on a finite interval. The Laws of the Iterated Logarithm for the Wiener process are established in Sect. 19.3. Section 19.4 is devoted to the Poisson processes, while Sect. 19.5 presents a characterisation of the class of processes with independent increments (the Lévy–Khintchin theorem).
CITATION STYLE
Borovkov, A. A. (2013). Processes with Independent Increments (pp. 539–557). https://doi.org/10.1007/978-1-4471-5201-9_19
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