What is it about?
We focus on investigating the strong convergence of Lévy-driven mixed stochastic integro-differential equations (L-mSIDEs) with singular kernels under the local Lipschitz and linear growth conditions. First, we transform the L-mSIDEs into an equivalent Lévy-driven mixed stochastic Volterra integral equations (L-mSVIEs) by a fractional calculus technique.
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Why is it important?
We rigorously analyze the existence, uniqueness, boundedness, and the continuous dependence of the analytical solutions to the L-mSVIEs. After that, we propose a modified stochastic Milstein method as a numerical solution for the L-mSVIEs by the local truncation technique and sum-of-exponentials (SOE) approximation scheme to improve the calculations effectively.
Perspectives
To study the applications in finance and economics.
Zhaoqiang Yang
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This page is a summary of: Strong convergence of Lévy-driven mixed stochastic integro-differential equations with application to the rough mixed volatility models, Communications on Analysis and Computation, January 2025, American Institute of Mathematical Sciences (AIMS),
DOI: 10.3934/cac.2025005.
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