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We consider a system of particles with locations
{Xn
i (t) : t ≥ 0, i = 1, . . . , n}
in Rd, time-varying weights {Ani
(t) : t ≥ 0, i = 1, . . . , n} and
weighted empirical measure processes V n(t)= 1
n n
i=1 Ani
(t)δXn
i
(t),
where δx is the Dirac measure. It is known that there exists the
limit of {Vn} in the week∗ topology onM(Rd) under suitable conditions.
If {Xn
i ,Ani
, V n} satisfies some diffusion equations, applying
Ito formula, we prove a central limit type theorem for the empirical
process {V n}, i.e., we consider the convergence of the processes
ηn
t ≡ √n(V n−V ). Besides, we study a characterization of its limit.
목차
등록된 정보가 없습니다.
참고문헌 (9)
참고문헌 신청
/ 1967 / Propogation of chaos for a class of non-linear parabolic equations 7
/ 1986 / Weak convergence of sequences of semimartingaleswith application to multitype branching processes 18
/ 1986. / Markov processes:Characterization and convergence
/ 1992 / Nonlinear Ito-Skorohod equations and martingale problem with dis-crete jump sets 40 : 6982 ~
/ 1994 / Asymptotic behavior of a system of interactingnuclear-space-valued stochastic dierential equation driven by Poisson randommeasures 30
/ 1986 / Weak convergence of sequences of semimartingaleswith application to multitype branching processes 18
/ 1986. / Markov processes:Characterization and convergence
/ 1992 / Nonlinear Ito-Skorohod equations and martingale problem with dis-crete jump sets 40 : 6982 ~
/ 1994 / Asymptotic behavior of a system of interactingnuclear-space-valued stochastic dierential equation driven by Poisson randommeasures 30
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