Related papers: Levy stable distributions via associated integral …
This article is devoted to derivation of the Laplace transforms of the derivatives with respect to parameters of certain special functions, namely, the Mittag-Leffler type, Wright and Le Roy type functions. These formulas show…
Process convolutions yield random fields with flexible marginal distributions and dependence beyond Gaussianity, but statistical inference is often hampered by a lack of closed-form marginal distributions, and simulation-based inference may…
For a spectrally negative L\'evy process $X$, we study the following distribution: $$ \mathbb{E}_x \left[ \mathrm{e}^{- q \int_0^t \mathbf{1}_{(a,b)} (X_s) \mathrm{d}s } ; X_t \in \mathrm{d}y \right], $$ where $-\infty \leq a < b < \infty$,…
The ordinary Levy motion is a random process whose stationary independent increments are statistically self-affine and distributed with a stable probability law characterized by the Levy index alpha, 0 < alpha < 2. The divergence of…
Superstatistics describes statistical systems that behave like superpositions of different inverse temperatures $\beta$, so that the probability distribution is $p(\epsilon_i) \propto \int_{0}^{\infty} f(\beta) e^{-\beta \epsilon_i}d\beta$,…
This paper considers the problem of estimating probabilities of the form $\mathbb{P}(Y \leq w)$, for a given value of $w$, in the situation that a sample of i.i.d.\ observations $X_1, \ldots, X_n$ of $X$ is available, and where we…
A novel approach towards construction of absolutely continuous distributions over the unit interval is proposed. Considering two absolutely continuous random variables with positive support, this method conditions on their convolution to…
We consider the problem of static Bayesian inference for partially observed Levy-process models. We develop a methodology which allows one to infer static parameters and some states of the process, without a bias from the…
We study the analytical properties of the Laplace transform of the lognormal distribution. Two integral expressions for the analytic continuation of the Laplace transform of the lognormal distribution are provided, one of which takes the…
We construct an efficient integrator for stochastic differential systems driven by Levy processes. An efficient integrator is a strong approximation that is more accurate than the corresponding stochastic Taylor approximation, to all orders…
A method for extracting the Levy stability index $\mu$ from the multi-fractal spectrum $f(\alpha)$ in high energy multiparticle production is proposed. This index is an important parameter, characterizing the non-linear behaviour of…
Exact results for the first passage time and leapover statistics of symmetric and one-sided Levy flights (LFs) are derived. LFs with stable index alpha are shown to have leapover lengths, that are asymptotically power-law distributed with…
Stable inverse systems for periodically time-varying plants are essential for feedforward control and iterative learning control of multirate and periodic systems, yet existing approaches either require complex-valued Floquet factors and…
We address the construction of stable random matrix ensembles as the generalization of the stable random variables (Levy distributions). With a simple method we derive the Cauchy case, which is known to have remarkable properties. These…
Approximating the optimal social welfare while preserving truthfulness is a well studied problem in algorithmic mechanism design. Assuming that the social welfare of a given mechanism design problem can be optimized by an integer program…
A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling…
The present paper studies a large class of temperature dependent probability distributions and shows that entropy and energy can be defined in such a way that these probability distributions are the equilibrium states of a generalized…
Inverse transform sampling is an exceptionally general method to generate non-uniform-distributed random numbers, but can be rather unstable when simulating extremely truncated distributions. Many famous probability models share a property…
We study the density of the supremum of a strictly stable L\'evy process. As was proved recently in F. Hubalek and A. Kuznetsov "A convergent series representation for the density of the supremum of a stable process" (Elect. Comm. in…
We develop new representations for the Levy measures of the beta and gamma processes. These representations are manifested in terms of an infinite sum of well-behaved (proper) beta and gamma distributions. Further, we demonstrate how these…