New Simplified High-Order Schemes for Solving SDEs with Markovian Switching Driven by Pure Jumps

New Simplified High-Order Schemes for Solving SDEs with Markovian Switching Driven by Pure Jumps

New high-order weak schemes are proposed and simplified to solve stochastic differential equations with Markovian switching driven by pure jumps (PJ-SDEwMs). Using Malliavin calculus theory, it is rigorously proven that the new numerical schemes can achieve a high-order convergence rate. Some numeri...

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Veröffentlicht in:Axioms 2024-03, Vol.13 (3), p.190
Hauptverfasser: Li, Yang, Xu, Yingmei, Xu, Qianhai, Zhang, Yu
Format: Artikel
Sprache:eng
Schlagworte:
Accuracy
Approximation
Calculus
Differential equations
Integrals
Malliavin calculus
Markov analysis
Markov processes
Markovian switching
Mathematical research
Numerical analysis
numerical scheme
pure jumps
Random variables
Stochastic differential equations
Stochastic models
Switching
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Beschreibung
Zusammenfassung:New high-order weak schemes are proposed and simplified to solve stochastic differential equations with Markovian switching driven by pure jumps (PJ-SDEwMs). Using Malliavin calculus theory, it is rigorously proven that the new numerical schemes can achieve a high-order convergence rate. Some numerical experiments are provided to show the efficiency and accuracy.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13030190