The mirror descent algorithm, originally conceived as a generalization of the gradient descent algorithm into non-Euclidean space, establishes a sophisticated framework that yields a profound geometric interpretation for optimizing problems across various domains. This study revolves around two primary contributions. Firstly, we delve into the stability analysis of the continuous-time mirrordescent algorithm, presenting a concise depiction of its equivalence to a projected dynamical system in a non-Euclidean domain—a nuanced generalization compared to continuous-time gradient descent. Secondly, we focus on the convergence of iterates in the stochastic mirror descent algorithm, elucidating its intricate relationship with the continuous-time counterpart. This dynamic perspective not only deepens our understanding of the stochastic mirror descent algorithm but also provides a foundation for robust analyses across diverse scenarios, with the added benefit of requiring fewer stringent assumptions.