A Multilevel birth-death particle system and its continuous diffusion
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In this paper we introduce a multilevel birth-death particle system and consider its diffusion approximation which can be characterized as aM([R+)-valued process. The tightness of rescaled processes is proved and we show that the limitingM(R+)-valued process is the unique solution of theM([R+)-valued martingale problem for the limiting generator. We also study the moment structures of the limiting diffusion process.
1993 ◽
Vol 25
(03)
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pp. 549-569
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2016 ◽
Vol 53
(3)
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pp. 783-801
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2020 ◽
Vol 16
(1)
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pp. 13-23
1999 ◽
Vol 51
(2)
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pp. 372-448
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1998 ◽
Vol 11
(3)
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pp. 289-300
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2016 ◽
Vol 371
(1699)
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pp. 20150128
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