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In probability theory relating to stochastic processes, a Feller process is a particular kind of Markov process. ==Definitions== Let ''X'' be a locally compact topological space with a countable base. Let ''C''0(''X'') denote the space of all real-valued continuous functions on ''X'' that vanish at infinity, equipped with the sup-norm ||''f'' ||. A Feller semigroup on ''C''0(''X'') is a collection ''t'' ≥ 0 of positive linear maps from ''C''0(''X'') to itself such that * ||''T''''t''''f'' || ≤ ||''f'' || for all ''t'' ≥ 0 and ''f'' in ''C''0(''X''), i.e., it is a contraction (in the weak sense); * the semigroup property: ''T''''t'' + ''s'' = ''T''''t'' o''T''''s'' for all ''s'', ''t'' ≥ 0; * lim''t'' → 0||''T''''t''''f'' − ''f'' || = 0 for every ''f'' in ''C''0(''X''). Using the semigroup property, this is equivalent to the map ''T''''t''''f'' from ''t'' in [0,∞) to ''C''0(''X'') being right continuous for every ''f''. Warning: This terminology is not uniform across the literature. In particular, the assumption that ''T''''t'' maps ''C''0(''X'') into itself is replaced by some authors by the condition that it maps ''C''b(''X''), the space of bounded continuous functions, into itself. The reason for this is twofold: first, it allows to include processes that enter "from infinity" in finite time. Second, it is more suitable to the treatment of spaces that are not locally compact and for which the notion of "vanishing at infinity" makes no sense. A Feller transition function is a probability transition function associated with a Feller semigroup. A Feller process is a Markov process with a Feller transition function. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Feller process」の詳細全文を読む スポンサード リンク
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