Superprocesses and their linear additive functionals
TL;DR: In this article, the authors consider Markov processes with nonstationary transition functions and derive integral and differential equations for the Laplace transforms of linear functions of the Markov process.
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Abstract: Let X=(X t ,P) be a measure-valued stochastic process. Linear functionals of X are the elements of the minimal closed subspace L of L 2 (P) which contains all X T (B) with ∫ X t (B) 2 dP<∞. We represent such functionals in terms of stochastic integrals and we derive integral and differential equations for their Laplace transforms. We consider Markov processes with nonstationary transition functions to reveal better the principal role of the backward equations
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Citations
Construction and regularity of measure-valued markov branching processes
TL;DR: In this paper, a construction for a general class of measure-valued Markov branching processes is given, where the underlying spatial motion process is an arbitrary Borel right Markov process and state-dependent offspring laws are allowed.
163
Propriétés de martingales, explosion et représentation de Lévy—Khintchine d'une classe de processus de branchement à valeurs mesures
Nicole El Karoui,Sylvie Roelly +1 more
TL;DR: In this paper, the authors studied martingale properties of a general class of measure-valued branching processes and obtained a Levy-Khintchine representation on the paths space and proposed an interpretation of the canonical measures in terms of entrance laws.
102
Infinitely Divisible Random Measures and Superprocesses
Donald A. Dawson
- 01 Jan 1992
TL;DR: In this article, the authors introduce the concept of local spatial clumping with a set of informal calculations that lead to the prediction that the continuous limit of branching particle systems in dimensions d ≥ 3 will lead to infinitely divisible random measures which are almost surely singular.
57
Some Limit Theorems for Super-Brownian Motion and Semilinear Differential Equations
TL;DR: In this paper, the empirical measure of super-Brownian motion was studied and it was shown that it tends almost surely to the Lebesgue measure as time $t \rightarrow \infty.
References
Sufficient Statistics and Extreme Points
TL;DR: In this article, the concept of sufficient statistics is used to prove that a set of functions or measures is a simplex, which is more convenient for many applications, instead of topological considerations.
•Book
Theory of Markov processes
E. B. Dynkin
- 01 Jan 2006
TL;DR: A method of polymerization of butadiene to form polymers with a high (greater than 90 percent) content of cis-1,4 configuration wherein a mixed fluoride bearing catalyst system is utilized to control the polymerization rate and the molecular weight is described in this paper.
191
Integral representation of excessive measures and excessive functions
TL;DR: Kifer and Pirogov as discussed by the authors obtained similar integral representations for the excessive measures and functions connected with an arbitrary Markov transition function in the language of convex measurable spaces and in contrast to previous papers no topological arguments are used.
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