Iterative weak approximation and hard bounds for switching diffusion

by   Qinjing Qiu, et al.

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.


page 1

page 2

page 3

page 4


Weak approximation for stochastic differential equations with jumps by iteration and hard bounds

We establish a novel theoretical framework in which weak approximation c...

Misinformation Mitigation under Differential Propagation Rates and Temporal Penalties

We propose an information propagation model that captures important temp...

Sparse Deep Neural Network for Nonlinear Partial Differential Equations

More competent learning models are demanded for data processing due to i...

Explicit approximations for nonlinear switching diffusion systems in finite and infinite horizons

Focusing on hybrid diffusion dynamics involving continuous dynamics as w...

Efficient simulation of DC-AC power converters using Multirate Partial Differential Equations

Switch-mode power converters are used in various applications to convert...