8,257 research outputs found
Correction to Black-Scholes formula due to fractional stochastic volatility
Empirical studies show that the volatility may exhibit correlations that
decay as a fractional power of the time offset. The paper presents a rigorous
analysis for the case when the stationary stochastic volatility model is
constructed in terms of a fractional Ornstein Uhlenbeck process to have such
correlations. It is shown how the associated implied volatility has a term
structure that is a function of maturity to a fractional power
Limit of Fractional Power Sobolev Inequalities
We derive the Moser-Trudinger-Onofri inequalities on the 2-sphere and the
4-sphere as the limiting cases of the fractional power Sobolev inequalities on
the same spaces, and justify our approach as the dimensional continuation
argument initiated by Thomas P. Branson.Comment: 17 page
Chaotic Inflation with a Fractional Power-Law Potential in Strongly Coupled Gauge Theories
Models of chaotic inflation with a fractional power-law potential are not
only viable but also testable in the foreseeable future. We show that such
models can be realized in simple strongly coupled supersymmetric gauge
theories. In these models, the energy scale during inflation is dynamically
generated by the dimensional transmutation due to the strong gauge dynamics.
Therefore, such models not only explain the origin of the fractional power in
the inflationary potential but also provide a reason why the energy scale of
inflation is much smaller than the Planck scale.Comment: 5 page
Fractional Integro-Differential Equations for Electromagnetic Waves in Dielectric Media
We prove that the electromagnetic fields in dielectric media whose
susceptibility follows a fractional power-law dependence in a wide frequency
range can be described by differential equations with time derivatives of
noninteger order. We obtain fractional integro-differential equations for
electromagnetic waves in a dielectric. The electromagnetic fields in
dielectrics demonstrate a fractional power-law relaxation. The fractional
integro-differential equations for electromagnetic waves are common to a wide
class of dielectric media regardless of the type of physical structure, the
chemical composition, or the nature of the polarizing species (dipoles,
electrons, or ions)
Modified Laplace transformation method at finite temperature: application to infra-red problems of N component theory
Modified Laplace transformation method is applied to N component
theory and the finite temperature problem in the massless limit is re-examined
in the large N limit. We perform perturbation expansion of the dressed thermal
mass in the massive case to several orders and try the massless approximation
with the help of modified Laplace transformation. The contribution with
fractional power of the coupling constant is recovered from the truncated
massive series. The use of inverse Laplace transformation with respect to the
mass square is crucial in evaluating the coefficients of fractional power
terms.Comment: 16pages, Latex, typographical errors are correcte
Fractional Derivative as Fractional Power of Derivative
Definitions of fractional derivatives as fractional powers of derivative
operators are suggested. The Taylor series and Fourier series are used to
define fractional power of self-adjoint derivative operator. The Fourier
integrals and Weyl quantization procedure are applied to derive the definition
of fractional derivative operator. Fractional generalization of concept of
stability is considered.Comment: 20 pages, LaTe
- …