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Periodic Solutions of Stochastic Functional Differential Equations with Jumps Via Viability

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Abstract

This paper concerns periodic solutions in distribution of stochastic functional differential equations with jumps. We obtain a comparison theorem by using viability and viscosity solutions as a tool. By applying the comparison theorem, we prove the existence of periodic solutions in distribution via the method of upper and lower solutions.

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Authors and Affiliations

  1. School of Mathematics and Statistics and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, 130024, People’s Republic of China

    ** Zhou & Yong Li

  2. School of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China

    **-Zhou-Aff1">** Zhou

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  3. **aomeng Jiang
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  4. Yong Li
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  5. Yuecai Han
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Correspondence to Yong Li.

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The second author was supported by NSFC (Nos. 11901231, 12071175), Special Funds of Provincial Industrial Innovation of Jilin Province China (No. 2017C028-1), Project of Science and Technology Development of Jilin Province China (No. 20190201302JC) and Natural Science Foundation of Jilin Province (No. 20200201253JC). The third author was supposed by National Basic Research Program of China (No. 2013CB834100), NSFC (No. 12071175), Special Funds of Provincial Industrial Innovation of Jilin Province China (No. 2017C028-1), Project of Science and Technology Development of Jilin Province China (No. 20190201302JC). The fourth author was supposed by NSFC (No. 11871244) and Project of Science and Technology Development of Jilin Province China (No. 20190201302JC)

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Zhou, X., Jiang, X., Li, Y. et al. Periodic Solutions of Stochastic Functional Differential Equations with Jumps Via Viability. J Dyn Diff Equat 34, 2429–2463 (2022). https://doi.org/10.1007/s10884-022-10139-0

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  • DOI: https://doi.org/10.1007/s10884-022-10139-0

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