A spine approach to branching diffusions with applications to L-p-convergence of martingales


Hardy, R. and Harris, S. C., 2009. A spine approach to branching diffusions with applications to L-p-convergence of martingales. Séminaire de Probabilités XLII, 1979, pp. 281-330.

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    We present a modified formalization of the 'spine' change of measure approach for branching diffusions in the spirit, of those found in Kyprianou [40] and Lyons et al. [44, 437 41]. We use our formulation to interpret certain 'Gibbs-Boltzmann' weightings of particles and use this to give an intuitive proof of a general 'Many-to-One' result which enables expectations of sums over particles in the branching diffusion to be calculated purely in terms of an expectation of one 'spine' particle. We also exemplify spine proofs of the L-p-convergence (p >= 1) of some key 'additive' martingales for three distinct models of branching diffusions including flew results for a multi-type branching Brownian motion and discussion of left-most particle speeds.


    Item Type Articles
    CreatorsHardy, R.and Harris, S. C.
    Uncontrolled Keywordselementary proofs, equation, exponential-growth, trees, limit-theorems, traveling-waves, brownian-motion, galton-watson processes
    DepartmentsFaculty of Science > Mathematical Sciences
    Publisher StatementHarris_SPXL11_2009_281.pdf: The original publication is available at
    ID Code15272


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