A semi-discrete and a fully discrete finite difference scheme for a reaction-diffusion PDE-ODE system with a Hölder stochastic boundary condition converge to the unique continuum solution, with the fully discrete theorem containing a residual gap.
Elliptic stochastic quantization of Sinh-Gordon QFT
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abstract
The (elliptic) stochastic quantization equation for the (massive) $\cosh(\beta \varphi)_2$ model, for the charged parameter in the $L^2$ regime (i.e. $\beta^2 < 4 \pi$), is studied. We prove the existence, uniqueness and the properties of the invariant measure of the solution to this equation. The proof is obtained through a priori estimates and a lattice approximation of the equation. For implementing this strategy we generalize some properties of Besov spaces in the continuum to analogous results for Besov spaces on the lattice. As a final result we show how to use the stochastic quantization equation to verify the Osterwalder-Schrader axioms for the $\cosh (\beta \varphi)_2$ quantum field theory, including the exponential decay of correlation functions.
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Discrete reaction-diffusion system with stochastic dynamical boundary conditions: convergence results
A semi-discrete and a fully discrete finite difference scheme for a reaction-diffusion PDE-ODE system with a Hölder stochastic boundary condition converge to the unique continuum solution, with the fully discrete theorem containing a residual gap.