Related papers: Functional Methods in Stochastic Systems
A tutorial review is given of some developments and applications of stochastic processes from the point of view of the practicioner physicist. The index is the following: 1.- Introduction 2.- Stochastic Processes 3.- Transient Stochastic…
A stochastic representation for the solutions of the Poisson-Vlasov equation, with several charged species, is obtained. The representation involves both an exponential and a branching process and it provides an intuitive characterization…
In this note we review recent results on existence and uniqueness of solutions of infinite-dimensional stochastic differential equations describing interacting Brownian motions on $\R^d$.
We present a theoretical approach to include dynamical aspects of molecular structural fluctuations, such as, for example, forming and breaking hydrogen bonds, isomerizations, and dynamical supramolecular structures, in nonequilibrium…
The key difficulty to develop efficient high-order methods for integrating stochastic differential equations lies in the calculations of the multiple stochastic integrals. This letter suggests a scheme to compute the stochastic integrals…
A functional differential equation related to the logistic equation is studied by a combination of numerical and perturbation methods. Parameter regions are identified where the solution to the nonlinear problem is approximated well by…
By constructing successful couplings, the derivative formula, gradient estimates and Harnack inequalities are established for the semigroup associated with a class of degenerate functional stochastic differential equations.
A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…
We review a recently-discovered link between the functional relations approach to integrable quantum field theories and the properties of certain ordinary differential equations in the complex domain.
In this paper it is shown how the generating functional for Green's functions in relativistic quantum field theory and in thermal field theory can be evaluated in terms of a standard quantum mechanical path integral. With this calculational…
In this paper we consider fractional higher-order stochastic differential equations of the form \begin{align*} \left( \mu + c_\alpha \frac{d^\alpha}{d(-t)^\alpha} \right)^\beta X(t) = \mathcal{E}(t) , \quad t\geq 0,\; \mu>0,\; \beta>0,\;…
Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…
In this paper we use a splitting technique to develop new multiscale basis functions for the multiscale finite element method (MsFEM). The multiscale basis functions are iteratively generated using a Green's kernel. The Green's kernel is…
A explicit formula on semiclassical Green functions in mixed position and momentum spaces is given, which is based on Maslov's multi-dimensional semiclassical theory. The general formula includes both coordinate and momentum representations…
We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical and, mechatronic systems. We derive the equations of motion for some typical mechatronic systems using deterministic principles…
The question in the title is ambiguous. At least the understanding of words essentially different and function theory should be clarified. We discuss approaches to do that. We also present a new framework for analytic function theories…
The disorder averaged single-particle Green's function of electrons subject to a time-dependent random potential with long-range spatial correlations is calculated by means of bosonization in arbitrary dimensions. For static disorder our…
On the basis of the tight-binding formalism and Green function technique we obtain all the Green functions matrix elements for a biased chain with a linear variation of the electron on-site energy. Their dependence on the system parameters…
A variational representation for functionals of G-Brownian motion is established by a finite-dimensional approximate technique. As an application of the variational representation, we obtain a large deviation principle for stochastic flows…
We propose a formalism to analyze discrete stochastic processes with finite-state-level N. By using an (N+1)-dimensional representation of su(2) Lie algebra, we re-express the master equation to a time-evolution equation for the state…