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We call peacock an integrable process which is increasing in the convex order; such a notion plays an important role in Mathematical Finance. A deep theorem due to Kellerer states that a process is a peacock if and only if it has the same one-dimensional marginals as a martingale. Such a martingale is then said to be associated to this peacock. In this monograph, we exhibit numerous examples of peacocks and associated martingales with the help of different methods: construction of sheets, time reversal, time inversion, self-decomposability, SDE, Skorokhod embeddings… They are developed in eight chapters, with about a hundred of exercises.
Business mathematics. --- Distribution (Probability theory). --- Negative binomial distribution. --- Martingales (Mathematics) --- Finance --- Distribution (Probability theory) --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Mathematical models --- Peafowl. --- Blue peafowl, Indian --- Common peafowl --- Indian blue peafowl --- Indian peafowl --- Pavo cristatus --- Peacocks --- Mathematics. --- Economics, Mathematical. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Quantitative Finance. --- Stochastic processes --- Pavo --- Distribution (Probability theory. --- Finance. --- Funding --- Funds --- Economics --- Currency question --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Economics, Mathematical . --- Mathematical economics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Methodology
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This reprint is a collection of papers on different aspects of the diversity and ecology of marine decapod crustaceans, including integrative taxonomy and genetic diversity, DNA barcoding to match larvae to adults, predator–prey interaction, coral–crab symbiosis, Sargassum–shrimp symbiosis, population dynamics of pelagic shrimps, diversity and distribution of oceanic larvae, spatial distribution of crabs, biodiversity of lobsters, and ecology of cave decapods. These contributions illustrate the variety of life forms, habitat use, and interspecific relationships exhibited by decapod crustaceans, one of the most diverse and abundant marine taxa.
Research & information: general --- Biology, life sciences --- cytochrome c oxidase subunit I (COI) --- larval dispersal --- mitochondrial genes --- molecular data --- 16S rRNA --- redescription --- Belzebub --- Lucifer --- sex ratio --- size structure --- size at first maturity --- population ecology --- symbiosis --- Sargassum shrimps --- chemical cues --- sponge shrimp --- coral cleaner shrimp --- taxonomy --- cytochrome oxidase 1 --- 16S ribosomal RNA --- association --- southwest Pacific Ocean --- ecology --- crustacean --- crab --- coral --- DNA barcoding --- Gulf of Mexico --- Caridea --- Dendrobranchiata --- Decapoda --- larval-adult matching --- life history --- decapods --- spiny lobsters --- slipper lobsters --- phyllosoma --- Caribbean Sea --- Yucatan Current --- lobster --- life cycle --- predator-prey --- food chain --- Brazil --- hermit crab --- Paguridae --- diversity --- molecular phylogeny --- species inventory --- zoogeography --- species richness --- depth preference --- cave zonation --- secondary stygobiosis --- trophic depletion --- protected species --- Cyclograpsus cinereus --- spatial distribution --- intertidal --- rocky shore --- negative binomial distribution --- n/a
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