A new modified model that combines the modified models of Chandrasekhar et al. with those of Keskin and Özgan, which are based on the Pople–Karasz theory, is applied to study the thermodynamics of melting and solid–solid transitions of molecular crystals. The thermodynamic properties of the...

We present a derivative pricing and estimation methodology for a class of stochastic volatility models that exploits the observed 'bursty' or persistent nature of stock price volatility. Empirical analysis of high-frequency S&P 500 index data confirms that volatility reverts slowly to its mean...

The principle of maximum entropy has been used to analyze the stability of the resulting process observed during the interaction of a random process with a 1/f spectrum and a deterministic action in lumped and distributed systems of nonlinear stochastic differential equations describing the...

We investigate arbitrary stochastic partial differential equations subject to translation invariant and temporally white noise correlations from a nonperturbative framework. The method that we expose first casts the stochastic equations into a functional integral form, then it makes use of the...

It is shown that, asymptotically, the behavior of a system of one-dimensional stochastic equations is the same whether one starts with a stationary solution or some initial state.

An analysis of master–slave hierarchy has been made in a system of nonlinear stochastic equations describing fluctuations with a 1/f spectrum at coupled nonequilibrium phase transitions. It is shown that for a system of stochastic equations there exist different probability distribution...

A formal theory of finding a nonlinear stochastic diffusion equation for density fluctuations in a suspension of colloidal hard spheres, which enables us to study the influence of solvent-mediated hydrodynamic interactions between particles as well as the direct interactions, is presented with...

We propose a model of fractal point process driven by the nonlinear stochastic differential equation. The model is adjusted to the empirical data of trading activity in financial markets. This reproduces the probability distribution function and power spectral density of trading activity...

We propose the point process model as the Poissonian-like stochastic sequence with slowly diffusing mean rate and adjust the parameters of the model to the empirical data of trading activity for 26 stocks traded on NYSE. The proposed scaled stochastic differential equation provides the universal...