Self-characteristic distributions

Characteristic Kernels and Infinitely Divisible Distributions

We connect shift-invariant characteristic kernels to infinitely divisible distributions on R. Characteristic kernels play an important role in machine learning applications with their kernel means to distinguish any two probability measures. The contribution of this paper is twofold. First, we show, using the Lévy–Khintchine formula, that any shift-invariant kernel given by a bounded, continuou...

Computability of Probability Distributions and Characteristic Functions

As a part of our works on effective properties of probability distributions, we deal with the corresponding characteristic functions. A sequence of probability distributions is computable if and only if the corresponding sequence of characteristic functions is computable. As for the onvergence problem, the effectivized Glivenko’s theorem holds. Effectivizations of Bochner’s theorem and de Moivr...

Characteristic Distributions in Multi-agent Systems*

In game theory, iterated strategic games are considered harder to analyze than repeated ones. However, iterated games are in many cases more fit to describe the situation of artificial agents than repeated games. The reason being that they take into account previous actions of others, rather than just assigning each possible action a certain probability. We introduce the notion of Characteristi...

Characteristic distributions of finite-time Lyapunov exponents.

We study the probability densities of finite-time or local Lyapunov exponents in low-dimensional chaotic systems. While the multifractal formalism describes how these densities behave in the asymptotic or long-time limit, there are significant finite-size corrections, which are coordinate dependent. Depending on the nature of the dynamical state, the distribution of local Lyapunov exponents has...

Characteristic functions of scale mixtures of multivariate skew-normal distributions