Jacod, J.; Shiryaev, A.N.: Limit theorems for stochastic prcesses, Springer-Verlag (1987).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....laws of (N n;l ) in ID( 0; T ] H 0 ) where H 0 is endowed with its weak topology. We proceed exactly as before, using Proposition 5.7. We prove moreover that the accumulations points of the laws of (N n;l ) charge only C( 0; T ] H 0 ) one says that the laws are C tight) Following [11], it suces to prove that the sequence sup s T kN n;l s N n;l s k 1 converges in probability to 0. It is easy to remark that for each 2 H, the jumps of N n;l : and of ; n;l : are at the same time and just two particles jump at every jump time. Then, if the jump takes place at time ....

....the martingale term and by adding the previous results, we nally obtain that each limit point is solution of (5. 16) Now let us prove that such a solution is unique in ID( 0; T ] H 0 ) The white noise W l is a Gaussian martingale with respect to the ltration generated by (W; l ) cf. [11] Prop. 1.12 p.484) Then we adapt to our context the Yamada Watanabe theorem and the pathwise uniqueness of (5.16) will imply the uniqueness in law. Now, let 1 and 2 two solutions of the equation. Then for ( p ) an orthonormal basis of H, and t T , k 1 t 2 t k 2 = X p ....

Jacod, J.; Shiryaev, A.N.: Limit theorems for stochastic prcesses, Springer-Verlag (1987).

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Jacod, J.; Shiryaev, A.N.: Limit theorems for stochastic prcesses, Springer-Verlag (1987).

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Jacod, J.; Shiryaev, A.N.: Limit theorems for stochastic prcesses, Springer-Verlag (1987).

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