Convergence of Locally Square Integrable Martingales to a Continuous Local Martingale
Let for each 𝑛∈ℕ𝑋𝑛 be an ℝ𝑑-valued locally square integrable martingale w.r.t. a filtration (ℱ𝑛(𝑡),𝑡∈ℝ+) (probability spaces may be different for different 𝑛). It is assumed that the discontinuities of 𝑋𝑛 are in a sense asymptotically small as 𝑛→∞ and the relation 𝖤(𝑓(⟨𝑧𝑋𝑛⟩(𝑡))|ℱ𝑛(𝑠))−𝑓(⟨𝑧𝑋𝑛⟩(𝑡))𝖯→0...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2011/580292 |
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