Abstract
We consider a measure-valued process that models a self-repelling or self-attracting population. The process is found as the unique solution to an equation driven by historical Brownian motion. The main result is pathwise uniqueness for a historical stochastic differential equation with a singular drift coefficient.
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Adler, R., Tribe, R. Uniqueness for a Historical SDE with a Singular Interaction. Journal of Theoretical Probability 11, 515–533 (1998). https://doi.org/10.1023/A:1022644108434
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DOI: https://doi.org/10.1023/A:1022644108434