The entanglement properties of the SU(1,1)-related coherent fields interacting with a moving atom via the two-photon transition are investigated. We discuss the quantum entanglement between the SU(1,1)-related coherent fields and the moving atom by using the quantum reduced entropy and that...

The distinguishability of particles has important implications for calculating the partition function in statistical mechanics. While there are standard formulations for systems of identical particles that are either fully distinguishable or fully indistinguishable, many realistic systems do not...

We obtain a non-linear generalization of the relativistic diffusion. We discuss diffusion equations whose non-linearity is a consequence of quantum statistics. We show that the assumptions of the relativistic invariance and an interpretation of the solution as a probability distribution...

Model or variable selection is usually achieved through ranking models according to the increasing order of preference. One of methods is applying Kullback–Leibler distance or relative entropy as a selection criterion. Yet that will raise two questions, why use this criterion and are there any...

The aim of this work is to take into account the effects of long memory in volatility on derivative hedging. This idea is an extension of the work by Fedotov and Tan [Stochastic long memory process in option pricing, Int. J. Theor. Appl. Finance 8 (2005) 381–392] where they incorporate...

We investigate the Heston model with stochastic volatility and exponential tails as a model for the typical price fluctuations of the Brazilian São Paulo Stock Exchange Index (IBOVESPA). Raw prices are first corrected for inflation and a period spanning 15 years characterized by memoryless...

In this paper, we extend a delayed geometric Brownian model by adding a stochastic volatility term, which is driven by a hidden process of fast mean reverting diffusion, to the delayed model. Combining a martingale approach and an asymptotic method, we develop a theory for option pricing under...

Multifractal random walks (MRW) correspond to simple solvable “stochastic volatility” processes. Moreover, they provide a simple interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that they are able to...

In this paper, we investigate a Langevin model subjected to stochastic intensity noise (SIN), which incorporates temporal fluctuations in noise-intensity. We derive a higher-order Fokker–Planck equation (HFPE) of the system, taking into account the effect of SIN by the adiabatic elimination...

Stochastic volatility models have been widely studied and used in the financial world. The Heston model (Heston, 1993)  [7] is one of the best known models to deal with this issue. These stochastic volatility models are characterized by the fact that they explicitly depend on a correlation...