The inverse tempered stable subordinator is a stochastic process that models power law waiting times between particle movements, with an exponential tempering that allows all moments to exist. This paper shows that the probability density function of an inverse tempered stable subordinator solves a tempered time-fractional diffusion equation, and its ‘‘folded’’ density solves a tempered time-fr...

We examine the evidence for the widespread belief that heavy tail distributions enhance the search for minima on multimodal objective functions. We analyze isotropic and anisotropic heavy-tail Cauchy distributions and investigate the probability to sample a better solution, depending on the step length and the dimensionality of the search space. The probability decreases fast with increasing st...

The effects of parametric uncertainty in stable state space systems are analyzed by averaging the state covariance over the statistics of the uncertain parameters. For natural frequency uncertainty, this computation is related to the Fourier transform of the probability density function of the uncertain parameter. Equipartition and incoherence are illustrated for a single mode oscillator. Avera...

AbstructWe develop a procedure for the order selection of damped sinusoidal models based on the maximum U posterion’ (MAP) criterion. The proposed method merges the concept of predictive densities with Bayesian inference to arrive at a complex multidimensional integral whose solution is achieved by way of the efficient Monte Carlo importance sampling technique. The importance function, a multiv...

We consider the problem of computing L1-distances between every pair of probability densities from a given family. We point out that the technique of Cauchy random projections [Ind06] in this context turns into stochastic integrals with respect to Cauchy motion. For piecewise-linear densities these integrals can be sampled from if one can sample from the stochastic integral of the function x 7→...

two statistical downscaling models, the non-homogeneous hidden markov model (nhmm) and the statistical down–scaling model (sdsm) were used to generate future scenarios of both mean and extremes in the tarim river basin,which were based on nine combined scenarios including three general circulation models (gcms) (csiro30, echam5,and gfdl21) predictor sets and three special report on emission sce...

we propose a method of estimation of the derivatives of probability density based on wavelets methods for a sequence of random variables with a common one-dimensional probability density function and obtain an upper bound on lp-losses for such estimators. we suppose that the process is strongly mixing and we show that the rate of convergence essentially depends on the behavior of a special quad...

Here, we propose a method of estimation of the derivatives of probability density based wavelets methods for a sequence of m−dependent random variables with a common one-dimensional probability density function and obtain an upper bound on Lp-losses for the such estimators.