In this paper, we extend Walsh’s stochastic integral with respect to a Gaussian noise, white in time and with some homogeneous spatial correlation, in order to be able to integrate some random measure-valued processes. This extension turns out to be equivalent to Dalang’s one. Then we study existence and regularity of the density of the probability law for the real-valued mild solution to a gen...

in this paper we consider a nonlinear two-phase stefan problem in one-dimensional space. the problem is mapped into a nonlinear volterra integral equation for the free boundary.

In this work we provide a direct calculation for nding the extended generator function of a regular step process, which is the solution of the stochastic integral equation known as the shock model.

We present a stochastic projection formalism for the description of quantum dynamics in bosonic or spin environments. The Schrödinger equation in the coherent state representation with respect to the environmental degrees of freedom can be reformulated by employing the Feshbach partitioning technique for open quantum systems based on the introduction of suitable non-Hermitian projection operato...

in this paper, a nonlinear volterra-fredholm integral equation of the first kind is solved by using the homotopy analysis method (ham). in this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by ham. the approximate solution of this equation is calculated in the form of a series which its components are computed easily. the accuracy...

in this paper, an iterative scheme for extracting approximate solutions of two dimensional volterra-fredholm integral equations is proposed. considering some conditions on the kernel of the integral equation obtained by discretization of the integral equation, the convergence of the approximate solution to the exact solution is investigated. several examples are provided to demonstrate the effc...

We study the treatment of the constraints in stochastic quantization method. We improve the treatment of the stochastic consistency condition proposed by Namiki et al. by suitably taking account of the Ito calculus. Then we obtain an improved Langevin equation and the Fokker-Planck equation which naturally leads to the correct path integral quantization of the constrained system as the stochast...

Lagrange multiplier methods are standard fare in elementary calculus courses, and they play a central role in economic applications of calculus because they often turn out to have interpretations as prices or shadow prices. You have seen them generalized to cover dynamic, non-stochastic models as Hamiltonian methods, or as byproducts of using Pontryagin’s maximum principle. In static models Lag...

Lagrange multiplier methods are standard fare in elementary calculus courses, and they play a central role in economic applications of calculus because they often turn out to have interpretations as prices or shadow prices. You have seen them generalized to cover dynamic, non-stochastic models as Hamiltonian methods, or as byproducts of using Pontryagin’s maximum principle. In static models Lag...