Unlocking solutions for stochastic heat equations! This paper tackles the challenge of solving stochastic heat equations where both the potential and initial conditions are generalized stochastic processes, pushing the boundaries of applied mathematics. The research constructs an explicit solution, rigorously demonstrating its existence within the generalized function space. This theoretical advancement provides a framework for understanding systems influenced by random fluctuations, with implications ranging from physics to finance. The explicit construction of the solution not only showcases the power of mathematical analysis but also opens doors for future research into complex stochastic systems, potentially offering new tools for modeling and predicting their behavior. This approach furthers the development of mathematical tools to understand systems affected by randomness. The paper's exploration of the stochastic heat equation and the Feynman–Kac formula within the framework of generalized stochastic processes provides new pathways for modeling complex phenomena.
Published in Infinite Dimensional Analysis, Quantum Probability and Related Topics, this paper aligns with the journal's focus on cutting-edge research in mathematical physics. By extending the Feynman-Kac formula to stochastic potentials, the work contributes to the understanding of quantum phenomena and probabilistic analysis, which are central themes of the journal. The references cited suggest a connection to existing research within the field, further solidifying the paper's relevance to the journal's readership.