{"product_id":"set-indexed-martingales-hardback","title":"Set-Indexed Martingales - Hardback","description":"\u003cp\u003eSet-Indexed Martingales offers a unique, comprehensive development of a general theory of Martingales indexed by a family of sets. The authors establish-for the first time-an appropriate framework that provides a suitable structure for a theory of Martingales with enough generality to include many interesting examples. \u003cbr\u003e\u003cbr\u003eDeveloped from first principles, the theory brings together the theories of Martingales with a directed index set and set-indexed stochastic processes. Part One presents several classical concepts extended to this setting, including: stopping, predictability, Doob-Meyer decompositions, martingale characterizations of the set-indexed Poisson process, and Brownian motion. Part Two addresses convergence of sequences of set-indexed processes and introduces functional convergence for processes whose sample paths live in a Skorokhod-type space and semi-functional convergence for processes whose sample paths may be badly behaved.\u003cbr\u003e\u003cbr\u003eCompletely self-contained, the theoretical aspects of this work are rich and promising. With its many important applications-especially in the theory of spatial statistics and in stochastic geometry- Set Indexed Martingales will undoubtedly generate great interest and inspire further research and development of the theory and applications.\u003c\/p\u003e","brand":"Taylor \u0026 Francis","offers":[{"title":"Default Title","offer_id":45565445701870,"sku":"9781584880820","price":184.8,"currency_code":"AUD","in_stock":true}],"url":"https:\/\/bookland.com.au\/products\/set-indexed-martingales-hardback","provider":"Book Land AU","version":"1.0","type":"link"}