Stochastic Partial Differential Equations: An Introduction

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The infinitesimal generator of the stochastic Burgers equation (2018, methodology): “The reason why the uniqueness proofs work is that we can linearize the equation via the Cole–Hopf transform: By formally applying Itô’s formula, we get u = ∂x logw, where w solves the stochastic heat equation ∂tw = w + √ 2wξ , a well posed equation which can be handled with classical SPDE approaches”
Global solutions to stochastic reaction–diffusion equations with super-linear drift and multiplicative noise (2019, background): “Several papers in the literature discuss stochastic pde’s with locally Lipschitz coefficients that have polynomial growth and/or satisfy certain monotonicity conditions (see [4, 12, 22], for instance).”
Well-posedness of stochastic partial differential equations with fully local monotone coefficients (2022, background): “5 in [55], we also know that X is an H-valued continuous process.”