Martingales with Independent Increments
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912146993971200 |
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| author | Delbaen, Freddy |
| author_facet | Delbaen, Freddy |
| contents | We show that a discrete time martingale with respect to a filtration with atomless innovations is the (infinite) sum of martingales with independent increments. For the continuous time filtration coming from Brownian Motion filtration, we show that every $L^2$ martingale is the sum of a series of Gaussian martingales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18716 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Martingales with Independent Increments Delbaen, Freddy Probability 60G42, 60G44 We show that a discrete time martingale with respect to a filtration with atomless innovations is the (infinite) sum of martingales with independent increments. For the continuous time filtration coming from Brownian Motion filtration, we show that every $L^2$ martingale is the sum of a series of Gaussian martingales. |
| title | Martingales with Independent Increments |
| topic | Probability 60G42, 60G44 |
| url | https://arxiv.org/abs/2406.18716 |