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We consider an infinite system of coupled stochastic differential equations(SDE) describing dynamics of the following infinite particle system. Eachpartricle is characterised by its position $x\in \mathbb{R}^{d}$ and internalparameter (spin) $\sigma _{x}\in \mathbb{R}$. While the positions of particlesform a fixed ("quenched") locally-finite set (configuration) $ \gamma \subset $$\mathbb{R}^{d}$, the spins $\sigma _{x}$ and $\sigma _{y}$ interact via a pairpotential whenever $\left\vert x-y\right\vert <\rho $, where $\rho >0$ is afixed interaction radius. The number $n_{x}$ of particles interacting with aparticle in positionn $x$ is finite but unbounded in $x$. The growth of $n_{x}$as $x\rightarrow \infty $ creates a major technical problem for solving our SDEsystem. To overcome this problem, we use a finite volume approximation combinedwith a version of the Ovsjannikov method, and prove the existence anduniqueness of the solution in a scale of Banach spaces of weighted sequences.As an application example, we construct stochastic dynamics associated withGibbs states of our particle system.

Stochastic dynamics of particle systems on unbounded degree graphs