Analysis of periodic solutions in Stratonovich stochastic lattice equations with Markovian switching, indicating unique existence under Lipschitz conditions.
In this paper, we study the Stratonovich stochastic lattice differential equations with the Markovian switching and jumps. The strong well‐posedness and weak uniqueness of solutions for such equations are shown under locally Lipschitz conditions. The comparison principle for solutions is established. Furthermore, the existence of periodic solutions in distribution is obtained by utilizing this result and the method of upper and lower solutions.
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Zhou et al. (2025) studied this question.
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