1. Abstract We study the stochastic quantization of two-dimensional nonlinear sigma model in the large N limit. Our main tool is the effective Langevin equation with which we investigate nonperturbative phenomena and derive the results which are same as the path integral approach gives.

In this paper we introduce a stochastic integral with respect to the solution X of the fractional heat equation on [0, 1], interpreted as a divergence operator. This allows to use the techniques of the Malliavin calculus in order to establish an Itô-type formula for the process X.

In this talk, we will introduce high accurate numerical schemes for solving forward backward stochastic differential equations (FBSDEs) with jumps. In these schemes, the simplest Euler scheme with only one jump is used to solve the forward stochastic differential equation (SDE), and multistep schemes is used to solve the backward stochastic differential equation (BSDE) with high convergence rat...

in this article, a transversely isotropic linear elastic half-space with depth wise isotropy axis of material containing a cylindrical cavity of finite length is considered to be under the effect of an arbitrary torsion force applied on the wall of the cavity. to this end, the equation of equilibrium has been written in a cylindrical coordinate system, by dividing the involved domain to two reg...

By using functional integral methods we determine new types of differential constraints satisfied by the joint probability density function of stochastic solutions to the wave equation subject to uncertain boundary and initial conditions. These differential constraints involve unusual limit partial differential operators and, in general, they can be grouped into two main classes: the first one ...

In stochastic modelling of flow in porous media, the medium properties that produce random trajectories of fluid elements are modelled by the assumed correlation kernel. For numerical simulation of the flow, the stochastic differential equation (SDE) is expanded using a Karhunen-Loeve expansion in terms of eigenvalues and eigenfunctions of the correlation function. In real world problems such a...

We present an approximate analytical expression for the escape rate of time-dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrateand-fire model for neural spiking. The novel approximation is based on a discrete state Markovian modeling of the full long-time dynamics with time-dependent rates. It is valid in a wide parameter regime beyond the restrai...

In this paper, we use the continuous Legendre wavelets on the interval [0,1] constructed by Razzaghi M. and Yousefi S. [6] to solve the linear second kind integral equations. We use quadrature formula for the calculation of the products of any functions, which are required in the approximation for the integral equations. Then we reduced the integral equation to the solution of linear algebraic ...

Starting with the Wigner function formulation for beam wave propagation in Hölder continuous non-Gaussian random refractive index fields we show that the wave beam regime naturally leads to the white-noise scaling limit and converges to a Gaussian Markovian model which is characterized the martingale problem associated to a stochastic differential-integral equation of the Ito type. In the geome...