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Iterative Weak Approximation and Hard Bounds for Switching Diffusion

Author

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  • Qinjing Qiu

    (University of Sydney)

  • Reiichiro Kawai

    (University of Sydney
    The University of Tokyo)

Abstract

We establish a novel convergent iteration framework for a weak approximation of general switching diffusion. The key theoretical basis of the proposed approach is a restriction of the maximum number of switching so as to untangle and compensate a challenging system of weakly coupled partial differential equations to a collection of independent partial differential equations, for which a variety of accurate and efficient numerical methods are available. Upper and lower bounding functions for the solutions are constructed using the iterative approximate solutions. We provide a rigorous convergence analysis for the iterative approximate solutions, as well as for the upper and lower bounding functions. Numerical results are provided to examine our theoretical findings and the effectiveness of the proposed framework.

Suggested Citation

  • Qinjing Qiu & Reiichiro Kawai, 2023. "Iterative Weak Approximation and Hard Bounds for Switching Diffusion," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1003-1036, June.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:2:d:10.1007_s10959-022-01185-x
    DOI: 10.1007/s10959-022-01185-x
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    References listed on IDEAS

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