Weak convergence of semimartingales and discretisation methods
AbstractGiven a semimartingale one can construct a system ([lambda], A, B, C) where [lambda] is the distribution of the initial value and (A, B, C) is the triple of global characteristics. Thus, given a process X and a system ([lambda], A, B, C) one can look for all probability measures P such that X is a P-semimartingale with initial distribution [lambda] and global characteristics (A, B, C). We say that such a measure P is a solution to the semimartingale problem ([lambda], A, B, C). The paper is devoted to the study of a special type of semimartingale problem. We look for sufficient conditions to insure the existence of solutions and we develop a method to construct them by means of time-discretised schemes, using weak topology for probability measures.
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Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 20 (1985)
Issue (Month): 1 (July)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
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