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A fractional stochastic path integral approach is presented as a natural framework for treating the random distribution of possible communication chains in the synaptic transmission of signals between initiator and distant target receptor neurons. Fractional Brownian motion parametrization is invoked to account for strong correlations between segments of a neuronal communication chain. We then obtain the probability density function (pdf) for the location of the target receptor neuron in terms of the Hurst index that classifies the dynamics into short-memory or long-memory domains. This pdf obtained by the path integral approach is a fundamental solution of the corresponding Fokker-Planck equation.

ON A FRACTIONAL STOCHASTIC PATH INTEGRAL APPROACH IN MODELLING INTERNEURONAL CONNECTIVITY