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When is Half‐Line Convergence to an Infinitely Divisible Law v Equivalent to Weak Convergence to v ?
Author(s) -
Ulanovskii A. M.
Publication year - 1998
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s002461079800581x
Subject(s) - convergence (economics) , mathematics , line (geometry) , law , real line , combinatorics , political science , economics , geometry , economic growth
For a wide class of infinitely divisible laws μ numbers R (μ) are evaluated satisfying the property: if R > R (μ) then μ is uniquely determined by its values on the half‐line (−∞, R ); if R < R (μ) then μ is not determined by its values on (−∞, R ). Necessary and sufficient conditions are given for ‘half‐line’ convergence to μ on (−∞, R ) to be equivalent to weak convergence to μ.