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Introductory Stochastic Analysis for Finance and Insurance by Society of Actuaries, X. Sheldon Lin

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CHAPTER 4

CONTINUOUS-TIME STOCHASTIC PROCESSES

4.1   GENERAL DESCRIPTION OF CONTINUOUS-TIME STOCHASTIC PROCESSES

Just as in the discrete-time case, the description of a continuous-time stochastic process begins with a time-dependent information structure or filtration {images, 0 ≤ tT}, on a probability space images. The information structure {images} satisfies the usual conditions:

(i)   For each t, images is an information structure containing no more information than images, and it represents the information up to time t ;

(ii)   If s < t, images contains no more information than images, i.e. all the events in images are events in images. In ...

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