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An extension of the Yamada‐Watanabe theorem
Author(s) -
Salavati Erfan
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4509
Subject(s) - mathematics , lipschitz continuity , monotonic function , extension (predicate logic) , uniqueness , mathematical analysis , comparison theorem , stochastic differential equation , picard–lindelöf theorem , fixed point theorem , computer science , programming language
Summary A well‐known result on pathwise uniqueness of the solution of stochastic differential equations in R is the Yamada‐Watanabe theorem. We have extended this result by replacing the Lipschitz assumption on the drift coefficient by much weaker assumption of semi‐monotonicity.