相关论文: On the factor ordering problem in stochastic infla…
The use of factor stochastic volatility models requires choosing the number of latent factors used to describe the dynamics of the financial returns process; however, empirical evidence suggests that the number and makeup of pertinent…
The minimal sub-Planckian axion inflation model accounts for a large scalar-to-tensor ratio via a spiralling trajectory in the field space of a complex field $\Phi$. Here we consider how the predictions of the model are modified by Planck…
We discuss the inflaton $\phi$ in an interaction with an infinite number of fields treated as an environment (noise) with a friction $\gamma^{2}>0$. In a Markovian approximation we obtain a stochastic wave equation (appearing also in the…
In this work we generalize a previously developed semiclassical approach to inflation, devoted to the analysis of the effective dynamics of coarse-grained fields, which are essential to the stochastic approach to inflation. We consider…
A class of linear evolutionary equations with material laws involving fractional time-derivatives is considered. The main result is well-posedness and causality for this problem class. The approach is illustrated with two examples: a…
Stochastic effects in generic scenarios of inflation with multiple fields are investigated. First passage time techniques are employed to calculate the statistical moments of the number of inflationary $e$-folds, which give rise to all…
A macroscopic universe may emerge naturally from a Planck cell fluctuation by unfolding through a stage of exponential expansion towards a homogeneous cosmological background. Such primordial inflation requires a large and presumably…
Natural (axionic) inflation can accommodate sizeable primordial tensor modes but suffers from the necessity of trans-Planckian variations of the inflaton field. This problem can be solved via the mechanism of aligned axions…
Fractional derivative in time variable is introduced into the Fokker-Planck equation of a population growth model. It's solution, the KNO scaling function, is transformed into the generating function for the multiplicity distribution.…
We make use of possible high energy correction to the Friedmann equation to implement the bounce and study the behavior of massive scalar field before and after bounce semianalytically and numerically. We find that the slow-roll inflation…
At the beginning of inflation there could be extra dynamical scalar fields that will soon disappear (become static) before the end of inflation. In the light of multi-field inflation, those extra degrees of freedom may alter the…
The main objective of this paper is to develop a martingale-type solution to optimal consumption--investment choice problems ([Merton, 1969] and [Merton, 1971]) under time-varying incomplete preferences driven by externalities such as…
Inflation may have been driven by a component which violated the Null-Energy Condition, thereby leading to {\it super inflation}. We provide the formalism to study cosmological perturbations when such a component is described by a scalar…
Scalar density cosmological perturbations, spectral indices and reheating in a chaotic inflationary universe model, in which a higher derivative term is added, are investigated. This term is supposed to play an important role in the early…
Using a long wavelength iteration scheme to solve Einstein's equations near the Big-Bang singularity of a universe driven by a massive scalar field, we find how big initial quasi-isotropic inhomogeneities can be before they can prevent…
In the present article, an approach to find the exact solution of the fractional Fokker-Planck equation is presented. It is based on transforming it to a system of first-order partial differential equation via Hopf transformation, together…
We study stochastic inflation in the presence of a dynamical gravitational constant. We describe the Arnowitt--Deser--Misner formalism for Jordan--Brans--Dicke theory of gravity with an inflaton field. The inflaton and dilaton scalar fields…
Defining a scale of $k$-modes of the quantum fluctuations during inflation through the dynamical horizon crossing condition $k = aH$ we go from the physical $t$ variable to $k$ variable and solve the equations of cosmological first-order…
We reconstruct scalar field theories to realize inflation compatible with the BICEP2 result as well as the Planck. In particular, we examine the chaotic inflation model, natural (or axion) inflation model, and an inflationary model with a…
The determination of acceptability prices of contingent claims requires the choice of a stochastic model for the underlying asset price dynamics. Given this model, optimal bid and ask prices can be found by stochastic optimization. However,…