188 research outputs found

    Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories

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    Extensive time-series encoding the position of particles such as viruses, vesicles, or individual proteins are routinely garnered in single-particle tracking experiments or supercomputing studies. They contain vital clues on how viruses spread or drugs may be delivered in biological cells. Similar time-series are being recorded of stock values in financial markets and of climate data. Such time-series are most typically evaluated in terms of time-averaged mean-squared displacements (TAMSDs), which remain random variables for finite measurement times. Their statistical properties are different for different physical stochastic processes, thus allowing us to extract valuable information on the stochastic process itself. To exploit the full potential of the statistical information encoded in measured time-series we here propose an easy-to-implement and computationally inexpensive new methodology, based on deviations of the TAMSD from its ensemble average counterpart. Specifically, we use the upper bound of these deviations for Brownian motion (BM) to check the applicability of this approach to simulated and real data sets. By comparing the probability of deviations for different data sets, we demonstrate how the theoretical bound for BM reveals additional information about observed stochastic processes. We apply the large-deviation method to data sets of tracer beads tracked in aqueous solution, tracer beads measured in mucin hydrogels, and of geographic surface temperature anomalies. Our analysis shows how the large-deviation properties can be efficiently used as a simple yet effective routine test to reject the BM hypothesis and unveil relevant information on statistical properties such as ergodicity breaking and short-time correlations. Video Abstract Video Abstract: Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectorie

    Computational methods for various stochastic differential equation models in finance

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    This study develops efficient numerical methods for solving jumpdiffusion stochastic delay differential equations and stochastic differential equations with fractional order. In addition, two novel algorithms are developed for the estimation of parameters in the stochastic models. One of the algorithms is based on the implementation of the Bayesian inference and the Markov Chain Monte Carlo method, while the other one is developed by using an implicit numerical scheme integrated with the particle swarm optimization
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