Iterative Weak Approximation and Hard Bounds for Switching Diffusion

Qinjing Qiu () and Reiichiro Kawai ()
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Qinjing Qiu: University of Sydney
Reiichiro Kawai: University of Sydney

Journal of Theoretical Probability, 2023, vol. 36, issue 2, 1003-1036

Abstract: 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.

Keywords: Continuous-time Markov chains; Diffusion processes; Recursive iterations; Hidden Markov model; Weakly coupled partial differential equations; 60J27; 60H10; 60J22; 65C30 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-022-01185-x

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