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<p>In this article, we study a nonlinear stochastic control problem perturbed by multiplicative Lévy noise, where the nonlinear operator&#xa0;(in divergence form) satisfies <i>p</i>-type growth with coercivity assumptions. By using Aldous tightness criteria and Jakubowski’s version of the Skorokhod theorem on non-metric spaces along with the standard <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="28_2024_1051_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation>-method, we establish the existence of a path-wise unique strong solution. Formulating the associated control problem, and using a variational approach together with the convexity property of cost functional (in control variable), we establish the existence of a weak optimal solution to the underlying problem. We use the technique of Maslowski and Seidler to prove an existence of an invariant measure for uncontrolled SPDE driven with multiplicative Lévy noise.</p>

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Nonlinear SPDE driven by Lévy noise: well-posedness, optimal control and invariant measure

  • 期刊论文

  • 发表日期：

    2025年1月8日

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  • R. Kavin,
  • Ananta K. Majee

摘要

In this article, we study a nonlinear stochastic control problem perturbed by multiplicative Lévy noise, where the nonlinear operator (in divergence form) satisfies p-type growth with coercivity assumptions. By using Aldous tightness criteria and Jakubowski’s version of the Skorokhod theorem on non-metric spaces along with the standard \(L^1\) L 1 -method, we establish the existence of a path-wise unique strong solution. Formulating the associated control problem, and using a variational approach together with the convexity property of cost functional (in control variable), we establish the existence of a weak optimal solution to the underlying problem. We use the technique of Maslowski and Seidler to prove an existence of an invariant measure for uncontrolled SPDE driven with multiplicative Lévy noise.