Re-weighted functional estimation of second-order diffusion processes

Metrika ◽  
2011 ◽  
Vol 75 (8) ◽  
pp. 1129-1151 ◽  
Author(s):  
Yunyan Wang ◽  
Lixin Zhang ◽  
Mingtian Tang
Keyword(s):  
Diffusion Processes ◽  
Second Order ◽  
Functional Estimation

scholarly journals A note on symmetries of diffusions within a martingale problem approach

2019 ◽  
Vol 19 (02) ◽  
pp. 1950011 ◽  
Author(s):  
Francesco C. De Vecchi ◽  
Paola Morando ◽  
Stefania Ugolini
Keyword(s):  
Diffusion Processes ◽  
Martingale Problem ◽  
Second Order ◽  
Lie Symmetries ◽  
Definition Of

A geometric reformulation of the martingale problem associated with a set of diffusion processes is proposed. This formulation, based on second-order geometry and Itô integration on manifolds, allows us to give a natural and effective definition of Lie symmetries for diffusion processes.

AVERAGING PRINCIPLE FOR QUASI-LINEAR PARABOLIC PDEs AND RELATED DIFFUSION PROCESSES

2012 ◽  
Vol 12 (01) ◽  
pp. 1150008 ◽  
Author(s):  
MARK FREIDLIN ◽  
LEONID KORALOV
Keyword(s):  
Small Parameter ◽  
Diffusion Processes ◽  
First Integral ◽  
Second Order ◽  
Averaging Principle ◽  
Two Dimensional ◽  
Parabolic Pdes ◽  
Dimensional Flow ◽  
Linear Perturbations ◽  
Two Dimensional Flow

Quasi-linear perturbations of a two-dimensional flow with a first integral and the corresponding parabolic PDEs with a small parameter at the second-order derivatives are considered in this paper.

scholarly journals Endüstriyel Sızıntı Suyundan Pb(II) Giderimi İçin Genleştirilmiş Perlit Kullanımı: Kinetik Çalışmalar

2018 ◽  
Vol 6 (3) ◽  
pp. 360
Author(s):  
Fulya Aydın Temel
Keyword(s):  
Kinetic Models ◽  
Diffusion Processes ◽  
Intraparticle Diffusion ◽  
Second Order ◽  
Expanded Perlite ◽  
Film Diffusion ◽  
Intraparticle Diffusion Model ◽  
Effects Of Ph ◽  
Pseudo Second Order ◽  
One Step

In this study, the removal efficiency of Pb(II) from industrial leachate was investigated by using expanded perlite by adsorption. The effects of pH, contact time, and adsorbent dosage were examined on the Pb(II) removal. The adsorption kinetics were tested to understand the adsorption mechanism using three kinetic models, i.e., Elovich, intraparticle diffusion, and the pseudo second order reaction kinetic models. As the result, the best conformity kinetic model for Pb(II) adsorption on expanded perlite was described as the pseudo second-order (R2>0.99). It is indicated that chemisorption is the determining step of adsorption process rather than mass transfer from industrial leachate. According to the data obtained from intraparticle diffusion model, the adsorption is composed of more than one step. This can be attributed to the fact that the adsorption in the final portion was the intraparticle diffusion while the adsorption in the first portion was the film diffusion. Both film diffusion and intraparticle diffusion processes in the adsorption of Pb(II) on expanded perlite are significant. This study indicated that expanded perlite was an influential alternative adsorbent for the removal of Pb(II) by adsorption from industrial leachate.

scholarly journals HOMOGENIZATION OF A PERIODIC DEGENERATE SEMILINEAR ELLIPTIC PDE

2011 ◽  
Vol 11 (02n03) ◽  
pp. 475-493 ◽  
Author(s):  
ÉTIENNE PARDOUX ◽  
AHMADOU BAMBA SOW
Keyword(s):  
Differential Operator ◽  
Weak Convergence ◽  
Diffusion Processes ◽  
Probabilistic Method ◽  
Second Order ◽  
Elliptic Pde ◽  
Semilinear Elliptic ◽  
Terminal Time ◽  
Oscillating Coefficients ◽  
Order Part

In this paper, a semilinear elliptic PDE with rapidly oscillating coefficients is homogenized. The novelty of our result lies in the fact that we allow the second order part of the differential operator to be degenerate in some portion of ℝd. Our fully probabilistic method is based on the connection between PDEs and BSDEs with random terminal time and the weak convergence of a class of diffusion processes.

LAGRANGIAN FEYNMAN FORMULAS FOR SECOND-ORDER PARABOLIC EQUATIONS IN BOUNDED AND UNBOUNDED DOMAINS

2010 ◽  
Vol 13 (03) ◽  
pp. 377-392 ◽  
Author(s):  
YANA A. BUTKO ◽  
MARTIN GROTHAUS ◽  
OLEG G. SMOLYANOV
Keyword(s):  
Parabolic Equations ◽  
Diffusion Processes ◽  
Unbounded Domains ◽  
Variable Coefficients ◽  
Second Order ◽  
Cauchy Problems ◽  
Elementary Functions ◽  
Functional Integrals ◽  
Finite Dimensional ◽  
Variable Diffusion

In this note a class of second-order parabolic equations with variable coefficients, depending on coordinate, is considered in bounded and unbounded domains. Solutions of the Cauchy–Dirichlet and the Cauchy problems are represented in the form of a limit of finite-dimensional integrals of elementary functions (such representations are called Feynman formulas). Finite-dimensional integrals in the Feynman formulas give approximations for functional integrals in the corresponding Feynman–Kac formulas, representing solutions of these problems. Hence, these Feynman formulas give an effective tool to calculate functional integrals with respect to probability measures generated by diffusion processes with a variable diffusion coefficient and absorption on the boundary.

scholarly journals A Second Order Approximation for Quasilinear Non-Fickian Diffusion Models

2013 ◽  
Vol 13 (4) ◽  
pp. 471-493 ◽  
Author(s):  
José A. Ferreira ◽  
Elias Gudiño ◽  
Paula de Oliveira
Keyword(s):  
Diffusion Processes ◽  
Order Approximation ◽  
Initial Boundary ◽  
Maxwell Model ◽  
Second Order ◽  
Fickian Diffusion ◽  
Uniform Grid ◽  
Singular Kernels ◽  
Second Order Convergence ◽  
Initial Boundary Value

Abstract. In this paper initial boundary value problems, defined using quasilinear diffusion equations of Volterra type, are considered. These equations arise for instance to describe diffusion processes in viscoelastic media whose behavior is represented by a Voigt–Kelvin model or a Maxwell model. A finite difference discretization defined on a general non-uniform grid with second order convergence order in space is proposed. The analysis does not follow the usual splitting of the global error using the solution of an elliptic equation induced by the integro-differential equation. The new approach enables us to reduce the smoothness required to the theoretical solution when the usual split technique is used. Non-singular and singular kernels are considered. Numerical simulations which show the effectiveness of the method are included.

scholarly journals NUMERICAL SOLUTION OF THE BOUNDARY PROBLEM FOR PARABOLIC EQUATION WITH NON-SELF-ADJOINT OPERATOR AND RELATED BOUNDARY CONDITIONS

2020 ◽  
pp. 7-11
Author(s):  
B. Dovgiy ◽  
L. Vakal ◽  
E. Vakal
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Diffusion Processes ◽  
Boundary Value ◽  
Adjoint Operator ◽  
Second Order ◽  
Algebraic Equations ◽  
Sweep Method ◽  
Linear Algebraic Equations

A boundary value problem for a second-order parabolic equation with a non-self-adjoint operator is considered. Such problems are mathematicalmodels for a number of problems, describing convective-diffusion processes of matter transfer, breakdown mechanisms of laser activity in plasma, etc. While studying the physics of breakdown, one should take into account the avalanche-like increase in the number of free electrons due to multiphoton ionization processes under the influence of optical pulses. This requires the inclusion of related boundary conditions in the problem formulation. An important circumstance that must be taken into account when developing a method for solving the problem is fulfillment of a certain conservation law for its solution. To solve the boundary value problem an approach based on the finite difference method is proposed. The approximation of the equation and boundary conditions is constructed so that the difference scheme is completely conservative. It approximates the original problem with the second order in the spatial variable and in time, and it has the second order of convergence. To effectively solve a system of linear algebraic equations at each time layer, the sweep method for complex systems in combination with the non-monotonic sweep method for systems with a tridiagonal matrix is used. Software based on computer mathematics MATLAB is developed to perform numerical calculations. It is obtained an approximate solution of an applied problem for different instants of time, as well as values of an absorption coefficient, the change in sign of which determines the transition of the plasma in a laser-active state.

scholarly journals ON THE FUNCTIONAL ESTIMATION OF MULTIVARIATE DIFFUSION PROCESSES

2017 ◽  
Vol 34 (4) ◽  
pp. 896-946 ◽  
Author(s):  
Federico M. Bandi ◽  
Guillermo Moloche
Keyword(s):  
Nonparametric Estimation ◽  
Asymptotic Theory ◽  
Diffusion Processes ◽  
Diffusion Matrix ◽  
Multivariate System ◽  
Functional Estimation ◽  
Conditional Expectations ◽  
Harris Recurrence ◽  
Asymptotic Mixed Normality ◽  
Recurrent Type

We propose a nonparametric estimation theory for the occupation density, the drift vector, and the diffusion matrix of multivariate diffusion processes. The estimators are sample analogues to infinitesimal conditional expectations constructed as Nadaraya-Watson kernel averages. Mild assumptions are imposed on the statistical properties of the multivariate system to obtain limiting results. Harris recurrence is all that we require to show consistency and asymptotic (mixed) normality of the proposed functional estimators. The identification method and asymptotic theory apply to both stationary and nonstationary multivariate diffusion processes of the recurrent type.

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