Abstract
A nonlocal stochastic model for intra- and extracellular proton dynamics in a tumor is proposed.The intracellular dynamics is governed by an SDE coupled to a reaction-diffusionequation for the extracellular proton concentration on the macroscale. In a more general contextthe existence and uniqueness of solutions for local and nonlocalSDE-PDE systems are established allowing, in particular, to analyze the proton dynamics model, bothin its local version and in the case with nonlocal path dependence.Numerical simulations are performedto illustrate the behavior of solutions, providing some insights into the effects of randomness on tumor acidity.
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