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Abstract: We prove the existence and uniqueness of a strong solution of a stochasticdifferential equation with normal reflection representing the random motion offinitely many globules. Each globule is a sphere with time-dependent randomradius and a center moving according to a diffusion process. The spheres arehard, hence non-intersecting, which induces in the equation a reflection termwith a local collision-time. A smooth interaction is considered too and, inthe particular case of a gradient system, the reversible measure of thedynamics is given. In the proofs, we analyze geometrical properties of theboundary of the set in which the process takes its values, in particular theso-called Uniform Exterior Sphere and Uniform Normal Cone properties. Thesetechniques extend to other hard core models of objects with a time-dependentrandom characteristic: we present here an application to the random motion of achain-like molecule.



Author: Myriam Fradon

Source: https://arxiv.org/



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