This paper proves the existence and uniqueness of quadratic mean almost periodic mild so-lutions for a class of stochastic dierential equations in a real separable Hilbert space. Themain technique is based upon an appropriate composition theorem combined with the Banachcontraction mapping principle and an analytic semigroup of linear operators.  

We discuss the problem of parameter estimation in nonlinear stochastic di€erential equations (SDEs) based on sampled time series. A central message from the theory of integrating SDEs is that there exist in general two time scales, i.e. that of integrating these equations and that of sampling. We argue that therefore, maximum likelihood estimation is computationally extremely expensive. We disc...

this paper proves the existence and uniqueness of quadratic mean almost periodic mild so-lutions for a class of stochastic dierential equations in a real separable hilbert space. themain technique is based upon an appropriate composition theorem combined with the banachcontraction mapping principle and an analytic semigroup of linear operators.

The problem of nding adapted solutions to systems of coupled linear forward-backward stochastic dierential equations (FBSDEs, for short) is investigated. A necessary condition of solvability leads to a reduction of general linear FBSDEs to a special one. By some ideas from controllability in control theory, using some functional analysis, we obtain a necessary and sucient condition for the solv...

Introduction Time discretization approximation schemes for solutions of stochastic dierential equations have been studied by many people and are treated, e.g. in the book of Kloeden-Platen [Kl-Pl92]. Since heat kernels are the probability densities of the law of solutions, it might be worthwhile to ask if these approximation schemes provide a natural scheme of approximation for heat kenrnels. P...

We present an AXIOM environment called JET for geometric computations with partial dierential equations within the framework of the jet bundle formalism. This comprises especially the completion of a given dierential equation to an involutive one according to the Cartan-Kuranishi Theorem and the setting up of the determining system for the generators of classical and non-classical Lie symmetrie...

in this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. we approximate the exact solution by use of radial basis function(rbf) collocation method. this techniqueplays an important role to reduce a fractional dierential equation to a system of equations. the numerical results demonstrate the accuracy and ability of this me...

In this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. We approximate the exact solution by use of Radial Basis Function(RBF) collocation method. This techniqueplays an important role to reduce a fractional dierential equation to a system of equations. The numerical results demonstrate the accuracy and ability of this me...

The Moving Finite Element method for the solution of time-dependent partial dierential equations is a numerical solution scheme which allows the automatic adaption of the nite element approximation space with time. An analysis of how this method models the steady solutions of a general class of parabolic linear source equations is presented. It is shown that the steady solutions of the Moving F...

Here, a new method called Aboodh transform homotopy perturbation method(ATHPM) is used to solve nonlinear partial dierential equations, we presenta reliable combination of homotopy perturbation method and Aboodh transformto investigate some nonlinear partial dierential equations. The nonlinearterms can be handled by the use of homotopy perturbation method. The resultsshow the eciency of this me...