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- W2084568013 abstract "The mapping x → x ̃ of D ([0, T ], S′ ( R d )) into S′ ( R d + 1 ) defined by 〈 x ̃ ,Φ〉 = ∫ 0 T 〈x(t),Φ(t,·)〉dt, Φ∈S(R d+1 ) is shown to be continuous. This is used to prove that for a tight sequence of processes ( X n ) inn in D ([0, T ], S′ ( R d )), weak convergence of ( X ̃ n ) n in S′ ( R d + 1 ) implies weak convergence of ( X n ). When [0, T ] is replaced by [0, ∞) the space S′ ( R d + 1 ) is not appropriate in general, and we investigate the question of what is the smallest nuclear space of distributions containing S′ ( R d + 1 ) that can be used. Our motivation comes from the asymptotic analysis of particle systems." @default.
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- W2084568013 date "1986-03-01" @default.
- W2084568013 modified "2023-09-27" @default.
- W2084568013 title "Convergence of S′-valued processes and space-time random fields" @default.
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- W2084568013 doi "https://doi.org/10.1016/0022-1236(86)90078-9" @default.
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