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This analysis investigates stochastic tracking outcomes in pursuer-evader dynamics, suggesting key conditions for success or failure.
We analyze a sufficient framework to predetermine the success or failure of stochastic asymptotic tracking in pursuer-evader dynamics. Specifically, we formulate a stochastic extension of the deterministic model studied in literature, which shares a similar interaction structure but lacks positive invariance. Within this setting, we establish conditions under which stochastic asymptotic tracking succeeds (pursuer winning) or fails (evader winning), providing both qualitative and quantitative characterizations of these regimes.
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Ahn et al. (2026) studied this question.
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