Systems of stochastic Poisson equations: Hitting probabilities

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I hope this article opens a window into the fascinating world of stochastic partial differential equations—an area often seen as highly theoretical and inaccessible. I would like to show that behind these complex systems lie crucial insights about randomness and uncertainty in spatial phenomena, which have implications far beyond mathematics alone. Understanding the behavior of solutions to elliptic stochastic equations, especially their hitting probabilities, is not just a dry, abstract concept but a key to unlocking how systems react under randomness—be it in physics, engineering, or finance. More than anything, I hope readers find this work inspiring and realize that rigorous analysis of such mathematical models can shed light on patterns and risks in the unpredictable real world. This kind of research is truly a bridge between elegant theory and practical challenges, and that is what makes it exciting to me.

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