Large datasets from a growing number of complex systems have been shown to exhibit a stochastic behavior that belongs to a class of white noise diffusion process with memory. A closed form for the probability density function for this class of diffusion processes can be obtained as a sum-over-all paths using the Hida white noise calculus. This framework can be used to uncover patterns, memory behavior, and mathematical relations in big datasets that could have several million data points. As examples, we start with the diffusion of microprobes in an ageing fibrin which could be important in tissue engineering and regenerative medicine, followed by a stochastic characterization of nucleotide distribution in a DNA sequence of bacterial genomes. The third example shows how the decreasing hard coral cover in the Great Barrier Reef share a common memory behavior with the ecological factors responsible for coral reef degradation such as sea surface temperature and increasing atmospheric CO2 levels. In all cases, a good match between empirical and theoretical mean square deviation and probability density functions are obtained.
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