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This is a Quantitative Study study.

October 13, 2025Open Access

Weak Existence and Uniqueness for Super-Brownian Motion with Irregular Drift

Key Points

Weak existence and uniqueness are established for the one-dimensional SPDE concerning super-brownian motion.
The proof utilizes an extension of the duality relation, focusing on admissible drifts that are irregular or discontinuous.
Incorporating functions that are non-Lipschitz allows for broader applications in stochastic partial differential equations.
These results enhance theoretical understanding of stochastic processes governed by irregular drift functions.

Abstract

We establish weak existence and uniqueness for random field solutions of the one-dimensional SPDE \ dₜXₜ = 12ΔXₜ +h (Xₜ) + XₜẆ, t 0, \ where Ẇ is space-time white noise and h is a bounded drift with h (0) 0. The proof relies on an extension of the duality relation of the super-Brownian motion, which allows us to treat a broad class of admissible drifts, including functions that are non-Lipschitz or discontinuous at zero.

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Cite This Study

Mytnik et al. (Sat,) studied this question.

synapsesocial.com/papers/68ecfebf950606aabec0930a https://doi.org/https://doi.org/10.48550/arxiv.2509.10984