A new expression for the characteristic function of log-spot in Heston model is presented. This expression more clearly exhibits its properties as an analytic characteristic function and allows us to compute the exact domain of the moment generating function. This result is then applied to the volatility smile at extreme strikes and to the control of the moments of spot. We also give a factoriz...

Abstract In this paper we introduce a fractional variant of the characteristic function random variable. It exists on whole real line, and is uniformly continuous. We show that moments can be expressed in terms Riemann–Liouville integrals derivatives function. The are interest particular for distributions whose integer do not exist. Some illustrative examples also presented.

This paper studies the injection process into a storage ring and presents an analytic model for the nonstationary particle distribution after m ismatched or off-axis injection. The effects of nonlinear fields as well as coupling to the longitudinal motion are described by analytic expressions for the first moments of the particle distribution. The result contains two distinct approximations: fi...

Characteristic polynomials of unitary matrices are extremely useful models for the Riemann zeta-function ζ(s). The distribution of their eigenvalues give insight into the distribution of zeros of the Riemann zeta-function and the values of these characteristic polynomials give a model for the value distribution of ζ(s). See the works [KS] and [CFKRS] for detailed descriptions of how these model...

A new approach to efficient blind image splicing detection is proposed in this paper. Image splicing is the process of making a composite picture by cutting and joining two or more photographs. The spliced image may introduce a number of sharp transitions such as lines, edges and corners. Phase congruency has been known as a sensitive measure of these sharp transitions and hence been proposed a...

The central moments of the multivariate normal distribution are functions of its n×n variance-covariance matrix Σ. These moments can be expressed symbolically as linear combinations of products of powers of the elements of Σ. A formula for these moments derived by differentiating the characteristic function is developed. The formula requires searching integer matrices for matrices whose n succe...

We study moments of characteristic polynomials truncated Haar distributed matrices from the three classical compact groups [Formula: see text], text] and text]. For finite matrix size we calculate in terms hypergeometric functions argument give explicit integral representations highlighting duality between moment as well orthogonal symplectic cases. Asymptotic expansions strong weak non-unitari...