By Doob’s theorem, supermartingales indexed by the natural numbers decompose into the difference of a uniformly integrable martingale and an increasing process. The relative ease of working with increasing processes rather than supermartingales explains the prominent role of this result in stochastic analysis and in the theory of stochastic integration. Meyer [19] then proved that, under the us...

Researchers show that network coding can greatly improve the quality of service in P2P live streaming systems (e.g., IPTV). However, network coding is vulnerable to pollution attacks where malicious nodes inject into the network bogus data blocks that will be combined with other legitimate blocks at downstream nodes, leading to incapability of decoding the original blocks and degradation of net...