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Regularity and Optimality Necessary Conditions for System of G-Stochastic Differential Equations

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Abstract

In the current paper, we deal with a system of G-stochastic differential equations (G-SDEs in short) driven by G-Brownian motion. Under some assumptions on the coefficients, we prove the temporal Hölder regularity of the solution. Moreover, we establish the Pontryagin’s maximum principle for optimal control of such system. An example is given to support the effectiveness of our main results.

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Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

  1. Department of Exact Sciences, École Normale Supérieure de Ouargla, 30000, Ouargla, Hai Ennasr, Algeria

    H. Ben Gherbal

  2. Laboratory of Probability and Statistics, Department of Mathematics, University of Badji Mokhtar, 23000, Annaba, Algeria

    A. Redjil

  3. Department of Chemistry, Laboratory of Researches in Radiations Physics and Their Interactions with Matter, Physics Department, Faculty of Matter Sciences, University of Hadj Lakhdar Batna, 05008, Batna, Algeria

    Z. Arab

Authors
  1. H. Ben Gherbal
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  2. A. Redjil
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  3. Z. Arab
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Corresponding authors

Correspondence to H. Ben Gherbal, A. Redjil or Z. Arab.

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Ben Gherbal, H., Redjil, A. & Arab, Z. Regularity and Optimality Necessary Conditions for System of G-Stochastic Differential Equations. Lobachevskii J Math 44, 4630–4642 (2023). https://doi.org/10.1134/S199508022311015X

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  • DOI: https://doi.org/10.1134/S199508022311015X

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