In this paper, 2D seismic data and petrophysical logs of the Pabdeh Formation from four wells of the Mansuri oil field are utilized. ΔLog R method was used to generate a continuous TOC log from petrophysical data. The calculated TOC values by ΔLog R method, used for a multi-attribute seismic analysis. In this study, seismic inversion was performed based on neural networks algorithm and the resu...

Večeř derived a degenerate parabolic equation with a boundary condition characterizing the price of Asian options for both discrete and continuous arithmetic average. It is well understood that there exists a unique probabilistic solution to such a problem. However, due to degeneracy of the partial differential operator and lack of smoothness in the boundary data, the regularity of the probabil...

In this paper we provide a new (probabilistic) proof of a classical result in partial differential equations, viz. if φ is a tempered distribution, then the solution of the heat equation for the Laplacian, with initial condition φ , is given by the convolution of φ with the heat kernel (Gaussian density). Our results also extend the probabilistic representation of solutions of the heat equation...

In this paper, we are interested in the one-dimensional porous medium equation when the initial condition is the distribution function of a probability measure. We associate a nonlinear martingale problem with it. After proving uniqueness for the martingale problem, we show existence owing to a propagation of chaos result for a system of weakly interacting di usion processes. The particle syste...

The Poisson-Boltzmann (PB) equation describes the electrostatic potential of a biomolecular system composed by a molecule in a solvent. The electrostatic potential is involved in biomolecular models which are used in molecular simulation. In consequence, nding an e cient method to simulate the numerical solution of PB equation is very useful. As a rst step, we establish in this paper a probabil...