A Wong-Zakai theorem for stochastic PDEs

By Martin Hairer, 'Etienne Pardoux. Journal of the Mathematical Society of Japan, 2014

207 citations recorded by the source corpus.

We prove a version of the Wong-Zakai theorem for one-dimensional parabolic nonlinear stochastic PDEs driven by space-time white noise. As a corollary, we obtain a detailed local description of solutions. Dedicated to the memory of Kiyosi It\^o on the occasion of the 100th anniversary of his birth.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d7b9318cd33e07e585c66163fe8c9213809a4b2f

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Citations in the corpus

A regularity structure for rough volatility (2017, methodology): “2 Hairer and Pardoux (2015) derive the KPZ result as special case of a Wong–Zakai result for Itô-SPDEs.”
HIGH ORDER PARACONTROLLED CALCULUS (2016, background): “One sees that they correspond to the terms needed to make sense of the products Z1ζ ; Z 2 1ζ, Z2ζ ; Z1Z2ζ, Z 3 1ζ, Z3ζ, in accordance with the overall picture provided by the theory of regularity structures – see Hairer and Pardoux work [20] for a study of equation (4.”
A CLASS OF GROWTH MODELS RESCALING TO KPZ (2015, methodology): “. This is avoided in the regularity structures approach [Hai13, Hai14] which, in principle, allows for many different types of regularization of the quadratic KPZ equation or stochastic heat equation [HP15]. At the present time it is however restricted to ﬁnite volume. Substantial progress has also ”
A diagram-free approach to the stochastic estimates in regularity structures (2021, methodology): “The comparison is easier for the semilinear multiplicative stochastic heat equation (∂2− ∂ 2 1 )u = a(u)ξ , as treated by tree-based regularity structures in [24] for α = (1)2−.”