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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Probability theory and related fields 56 (1981), S. 399-414 
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The main results of the paper concern integral representations of convex sets of probability laws. Various types of simplices are introduced and characterized. Invariance with respect to Markovian operators plays a key rôle.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 100 (1985), S. 85-103 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a locally Lipschitz continuous mappingF between metric spacesZ andX and probability measures μ, ν onZ, bounds for the (Prokhorov and bounded Lipschitz) distance of μF −1 and νF −1 are obtained in terms of the distance of μ and ν, the growth of the local Lipschitz constants ofF, and a tail estimate of μ. As applications, we estimate convergence rates of approximate solutions of stochastic differential euqations and obtain conditions on the speed of convergence of regularization parameters which guarantee convergence in distribution for the solutions of a random integral equation of the first kind.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1572-9036
    Keywords: Primary: 60G55, 60G57 ; Secondary: 60J80, 35J60 ; Branching particle system ; superprocess ; equilibrium ; persistence ; nonlinear partial differential equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a class of multitype particle systems in ℝ d undergoing spatial diffusion and critical stable multitype branching, and their limits known as critical stable multitype Dawson-Watanabe processes, or superprocesses. We show that for large classes of initial states, the particle process and the superprocess converge in distribution towards known equilibrium states as time tends to infinity. As an application we obtain the asymptotic behavior of a system of nonlinear partial differential equations whose solution is related to the distribution of both the particle process and the superprocess.
    Type of Medium: Electronic Resource
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