  The non-Hermitian skin effect refers to the accumulation of eigenstates near
the boundary in open boundary lattice models, which can be systematically
characterized using the non-Bloch band theory. Here, we apply the non-Bloch
band theory to investigate the stochastic reaction-diffusion process by mapping
it to a non-Hermitian Kitaev chain. We exactly obtain the open boundary
spectrum and the generalized Brillouin zone, and identify a robust zero mode
arising from the non-Bloch topology. Notably, distinct from its Hermitian
counterpart in the quantum context, the zero mode supports anomalous dynamical
crossover in the Markov process. We quantitatively demonstrate the intriguing
dynamical effects through the spectral decomposition of the Hamiltonian on the
non-Bloch eigenstates, and confirm our findings by conducting stochastic
simulations with high accuracy. Our study highlights the significant and
general role of non-Bloch topology in non-equilibrium dynamics.
