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<p>The existence-uniqueness theory for solutions to stochastic dynamic systems is always a significant theme and has received tremendous attention. This article aims to study the theory for stochastic functional differential equations (SFDEs) driven by the G-Lévy process. It derives the existence-uniqueness theorem for solutions to SFDEs driven by the G-Lévy process. Moreover, it shows the error estimation between the exact solution <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13662_2024_3856_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>x</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$x(t)$</EquationSource> </InlineEquation> and Picard approximate solutions <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13662_2024_3856_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="86" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msup> <mi>x</mi> <mi>n</mi> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mi>n</mi> <mo>≥</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$x^{n}(t), n\geq 1$</EquationSource> </InlineEquation>. Ultimately, the exponential estimate has been derived.</p>

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On the existence-uniqueness and exponential estimate for solutions to stochastic functional differential equations driven by G-Lévy process

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月7日

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  • Rahman Ullah,
  • Faiz Faizullah,
  • Ihteram Ali,
  • Muhammad Farooq,
  • M. A. Rana,
  • Fuad A. Awwad

摘要

The existence-uniqueness theory for solutions to stochastic dynamic systems is always a significant theme and has received tremendous attention. This article aims to study the theory for stochastic functional differential equations (SFDEs) driven by the G-Lévy process. It derives the existence-uniqueness theorem for solutions to SFDEs driven by the G-Lévy process. Moreover, it shows the error estimation between the exact solution x ( t ) $x(t)$ and Picard approximate solutions x n ( t ) , n ≥ 1 $x^{n}(t), n\geq 1$ . Ultimately, the exponential estimate has been derived.