2006
DOI: 10.1214/154957806000000104
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An essay on the general theory of stochastic processes

Abstract: This text is a survey of the general theory of stochastic processes, with a view towards random times and enlargements of filtrations. The first five chapters present standard materials, which were developed by the French probability school and which are usually written in French. The material presented in the last three chapters is less standard and takes into account some recent developments.

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Cited by 76 publications
(47 citation statements)
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“…The last condition combined with the assumption Z ∞ = 0 implies [10] for more discussion on such a situation). Consequently, if the Föllmer measure Q F is a solution for Problem P, the P − F local martingale N must be the constant 1, a situation covered by the Cox measure.…”
Section: Föllmer's Measurementioning
confidence: 99%
“…The last condition combined with the assumption Z ∞ = 0 implies [10] for more discussion on such a situation). Consequently, if the Föllmer measure Q F is a solution for Problem P, the P − F local martingale N must be the constant 1, a situation covered by the Cox measure.…”
Section: Föllmer's Measurementioning
confidence: 99%
“…To remedy this difficulty, we may use the fact that the stopping time ϱ is predictable, as every stopping time in a Brownian filtration is predictable (see e.g. [29,Example 4.12]). We therefore may find an increasing sequence (ϱ n ) ∞ n=1 of announcing stopping times, i.e., ϱ n < ϱ and lim n→∞ ϱ n = ϱ, almost surely.…”
mentioning
confidence: 99%
“…The following classical lemma will be very helpful: it indicates the properties of the above processes under the assumptions (A) or (C) (for more details or references, see Dellacherie, Maisonneuve, and Meyer 1992 or Nikeghbali 2006).…”
mentioning
confidence: 99%