Authors: Kim Ju Gyong，Ju Kwang Son
Comments: 7 Pages.
In this paper we prove Girsanov theorem for fractional Brownian motion and jump
measures and consider representation form for the stochastic differential equations in
transfer Probability space.
Authors: Russell Leidich
Comments: 13 Pages.
Successive real-valued measurements of any physical chaotic oscillator can serve as entropy inputs to a random number generator (RNG) with correspondingly many whole numbered outputs of arbitrarily small bias, assuming that no correlation exists between successive such measurements apart from what would be implied by their probability distribution function (AKA the oscillator’s analog “generator”, which is constant over time and thus asymptotically discoverable).
Given some historical measurements (a “snapshot”) of such an oscillator, we can then train the RNG to expect inputs distributed uniformally among the real intervals defined by those measurements and spanning the entire real line. Each interval thus implies an index in sorted order, starting with the leftmost which maps to zero; the RNG does nothing more than to perform this mapping. We can then replace that first oscillator with a second one presumed to abide by the same generator. It would then be possible to characterize the accuracy of that presumption by quantifying the ensuing change in quality of the RNG.
Randomness quality is most accurately expressed via dyspoissonism, which is a normalized equivalent of the log of the number of ways in which a particular distribution of frequencies (occurrence counts) of masks (whole numbers) can occur. Thus the difference in dyspoissonism between the RNG output sets will serve to estimate the information divergence between theirrespective generators, which in turn constitutes a ranking quantifier for the purpose of anomaly detection.