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Extension to infinite dimensions of a stochastic second-order model associated with shape splines

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  • Vialard, François-Xavier

Abstract

Motivated by the development of a probabilistic model for growth of biological shapes in the context of large deformations by diffeomorphisms, we present a stochastic perturbation of the Hamiltonian equations of geodesics on shape spaces. We study the finite-dimensional case of groups of points for which we prove that the strong solutions of the stochastic system exist for all time. We extend the model to the space of parameterized curves and surfaces and we develop a convenient analytical setting to prove a strong convergence result from the finite-dimensional to the infinite-dimensional case. We then present some enhancements of the model.

Suggested Citation

  • Vialard, François-Xavier, 2013. "Extension to infinite dimensions of a stochastic second-order model associated with shape splines," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2110-2157.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:6:p:2110-2157
    DOI: 10.1016/j.spa.2013.01.012
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    References listed on IDEAS

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    1. Yvo Pokern & Andrew M. Stuart & Petter Wiberg, 2009. "Parameter estimation for partially observed hypoelliptic diffusions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 49-73, January.
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