Jacobian bounds, functional inequalities, and dispersion for stochastic differential equations with interaction

Kyrylo Kuchynskyi
Theory of Stochastic Processes
Vol.30 (46), no.1, 2026, pp.15-32

We study evolutions of measures under flows of solutions to stochastic differential equations with interaction. Under suitable regularity assumptions on the coefficients, we prove moment bounds for the compact-set Jacobian norm. These bounds yield pathwise transfer of logarithmic Sobolev, concentration, and Talagrand transport inequalities from the initial measure to the random pushforward measure at time t. Finally, for a kernel model satisfying a pairwise dissipativity condition, we prove exponential decay of the expected dispersion around the random center of mass.

DOI: https://doi.org/10.3842/tsp-7021016408-54
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