Questions tagged [stochastic-pde]

Stochastic partial differential equations are partial differential equations with a random driving force. Please do not use this tag just because there are stochastic processes and differential equations in your question. Consider if [tag: SDE] is a better choice. This tag is only to be used for PDEs driven by noise.

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Proof of unique existence of Stochastic Wave Equation (d=1)

I'm trying to prove the uniqueness and existence of the solution for the following Stochastic Wave Equation in one-spatial dimension as follows: $ \frac{d^{2}u}{dt^{2}} - \frac{d^{2}u}{dt^{2}} = \sigma(u(t,x))\dot{W}(t,x),\ t \in [0,T]$ (where…
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How to obtain the formal scaling for the following PDE?

In the paper by Mourrat and Weber( GLOBAL WELL-POSEDNESS OF THE DYNAMIC $\Phi^4_3$ MODEL ON THE TORUS) one reads: Equation (1.1) is given by: I couldn't arrive at (1.3) Attempt: note that $\partial_{\hat t} = \lambda^2 \partial_t $ and…