We propose a Stochastic Formulation that establishes a direct mathematical correspondence between the real-time Feynman path integral in Minkowski spacetime and the expectation values of classical stochastic processes. This framework offers an alternative approach to quantum dynamics by formulating evolution through intrinsic stochastic processes rather than relying solely on pre-discretized spacetime backgrounds. Specifically, we demonstrate that the unitary dynamics of scalar fields can be mapped to continuous Wiener processes, while spinor fields correspond to discrete Poisson jump processes. Distinct from conventional methods involving perturbative expansions, Euclideanization, or Grassmann algebra, our formulation provides a non-perturbative, real-time framework where quantum amplitudes are derived statistically from stochastic trajectories.We implement this framework via a grid-based tree recursion scheme for the Klein-Gordon field, benchmarked against exact solutions of the forced harmonic oscillator. For the Dirac field, we derive an analytical closed-form finite difference scheme that effectively models its evolution. By integrating these schemes, we successfully apply the framework to the Yukawa coupling model and extend it to QED. Our results reveal non-trivial dynamical features, such as feedback-driven mass oscillations, offering complementary insights to standard perturbative descriptions. Crucially, the structural nature of this stochastic approach inherently avoids the fermion doubling and sign problems often encountered in lattice approach. These applications suggest a robust pathway for tackling complex systems, including gauge theories like QCD.