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Central limit type theorem for weighted particle systems
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Abstract
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.
참고문헌 (9)
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