Journal article
Adapted topologies and higher rank signatures
- Abstract:
- The topology of weak convergence does not account for the growth of information over time that is captured in the filtration of an adapted stochastic process. For example, two adapted stochastic processes can have very similar laws but give completely different results in applications such as optimal stopping, queuing theory, or stochastic programming. To address such discontinuities, Aldous introduced the extended weak topology, and subsequently, Hoover and Keisler showed that both, weak topology and extended weak topology, are just the first two topologies in a sequence of topologies that get increasingly finer. We use higher rank expected signatures to embed adapted processes into graded linear spaces and show that these embeddings induce the adapted topologies of Hoover–Keisler.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
Actions
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- Files:
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(Preview, Accepted manuscript, pdf, 457.9KB, Terms of use)
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- Publisher copy:
- 10.1214/22-AAP1862
Authors
- Publisher:
- Institute of Mathematical Statistics
- Journal:
- Annals of Applied Probability More from this journal
- Volume:
- 33
- Issue:
- 3
- Pages:
- 2136-2175
- Publication date:
- 2023-05-02
- Acceptance date:
- 2022-06-14
- DOI:
- ISSN:
-
1050-5164
Terms of use
- Copyright holder:
- Institute of Mathematical Statistics
- Copyright date:
- 2023
- Rights statement:
- © 2023 Institute of Mathematical Statistics
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Institute of Mathematical Statistics at: https://doi.org/10.1214/22-AAP1862
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