4.6 Article

Scaling limit of stretched Brownian chains

出版社

IOP Publishing Ltd
DOI: 10.1088/1751-8121/acfd6d

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Gaussian process; Ornstein-Uhlenbeck process; interacting particle system; stochastic heat equation

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This study demonstrates that a properly scaled stretched long Brownian chain converges to a two-parametric stochastic process, which is the sum of an explicit deterministic continuous function and the solution of the stochastic heat equation with zero boundary conditions.
We show that a properly scaled stretched long Brownian chain converges to a two-parametric stochastic process, given by the sum of an explicit deterministic continuous function and the solution of the stochastic heat equation with zero boundary conditions.

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