Limit Theorems for Superprocesses: Rescaled Processes, Immigration Superprocesses and Homogeneous Superprocesses - Softcover

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9783659521201: Limit Theorems for Superprocesses: Rescaled Processes, Immigration Superprocesses and Homogeneous Superprocesses
Softcover
ISBN 10: 3659521205 ISBN 13: 9783659521201
Verlag: LAP LAMBERT Academic Publishing, 2014

Inhaltsangabe

This monograph treats recent results on limit theorems for superprocesses (SPs). Chapter 1 is devoted to a class of SPs with deterministic immigration, and deals with a convergence problem for rescaled processes. When such an SP with dependent spatial motion (SDSM) is given, under a proper scaling the rescaled SPs converge to an SP with coalescing spatial motion (SCSM) in the sense of probability distribution on the space of measure-valued continuous paths (pdmc). In Chapter 2 we discuss a distinct convergence problem for a class of SDSMs with deterministic immigration rate. When the immigration rate converges to a non-vanishing deterministic one, then we can prove that under a suitable scaling, the rescaled SPs associated with SDSM converge to a class of immigration SPs associated with SCSM in the sense of pdmc. This rescaled limit does not provide only with a new class of SPs but gives also a new type of limit theorem. A class of homogeneous SPs of diffusion type with spatially dependent parameters and its asymptotic behaviors are discussed in Chapter 3. If the underlying diffusion is recurrent, we prove a limit theorem on the moment of such SPs as time t goes to infinity.

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Reseña del editor

This monograph treats recent results on limit theorems for superprocesses (SPs). Chapter 1 is devoted to a class of SPs with deterministic immigration, and deals with a convergence problem for rescaled processes. When such an SP with dependent spatial motion (SDSM) is given, under a proper scaling the rescaled SPs converge to an SP with coalescing spatial motion (SCSM) in the sense of probability distribution on the space of measure-valued continuous paths (pdmc). In Chapter 2 we discuss a distinct convergence problem for a class of SDSMs with deterministic immigration rate. When the immigration rate converges to a non-vanishing deterministic one, then we can prove that under a suitable scaling, the rescaled SPs associated with SDSM converge to a class of immigration SPs associated with SCSM in the sense of pdmc. This rescaled limit does not provide only with a new class of SPs but gives also a new type of limit theorem. A class of homogeneous SPs of diffusion type with spatially dependent parameters and its asymptotic behaviors are discussed in Chapter 3. If the underlying diffusion is recurrent, we prove a limit theorem on the moment of such SPs as time t goes to infinity.

Biografía del autor

Took his Ph.D. in Probability Theory at University of Tsukuba. Professor at Saitama University, Japan. His field of study: stochastic partial differential equations, white noise analysis, and superprocesses. Author of "Probability and Statistics" (in Japanese) in Math Textbook Ser., Sugakushobo, Tokyo. A member of the Mathematical Society of Japan.

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Verlag
LAP LAMBERT Academic Publishing
Erscheinungsdatum
2014
Sprache
Englisch
ISBN 10 
3659521205
ISBN 13 
9783659521201
Einband
Tapa blanda
Anzahl der Seiten
128
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