Threshold Diffusions

Published 25 Aug 2025 in math.PR | (2508.17812v1)

Abstract: We propose threshold diffusion processes as unique solutions to stochastic differential equations with step-function coefficients, and obtain explicit expressions for the conditional Laplace transform of the hitting times and the potential measures. Applying these results, we further discuss their asymptotic behaviors such as the stationary distributions and the escape probabilities.

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