DIFFUSION PROCESSES ON PATH SPACES WITH INTERACTIONS

2001 ◽  
Vol 13 (02) ◽  
pp. 199-220 ◽  
Author(s):  
YUU HARIYA ◽  
HIROFUMI OSADA
Keyword(s):  
Diffusion Processes ◽  
Gibbs Measures ◽  
Infinite Volume ◽  
Gaussian Measures ◽  
Uhlenbeck Process ◽  
Mild Conditions ◽  
Carré Du Champ ◽  
Form Theory ◽  
The One ◽  
Non Gaussian

We construct dynamics on path spaces C (ℝ; ℝ) and C([-r, r];ℝ) whose equilibrium states are Gibbs measures with free potential φ and interaction potential ψ. We do this by using the Dirichlet form theory under very mild conditions on the regularity of potentials. We take the carré du champ similar to the one of the Ornstein–Uhlenbeck process on C([0, ∞);ℝ). Our dynamics are non-Gaussian because we take Gibbs measures as reference measures. Typical examples of free potentials are double-well potentials and interaction potentials are convex functions. In this case the associated infinite-volume Gibbs measures are singular to any Gaussian measures on C(ℝ;ℝ).

Production of novel carbon nanostructures by electrochemical reduction of polychlorinated organic rings under mild conditions for supercapacitors

2021 ◽  
Author(s):  
Züleyha Kudaş ◽  
Emir Çepni ◽  
Emre Gür ◽  
Duygu Ekinci
Keyword(s):  
Carbon Source ◽  
Electrochemical Reduction ◽  
Electrochemical Method ◽  
Carbon Nanostructures ◽  
Electrochemical Growth ◽  
Mild Conditions ◽  
One Step ◽  
The One ◽  
Carbon Based

Here, new carbon-based nanostructures were prepared by the one-step electrochemical method using hexagonal and pentagonal polychlorinated organic rings as carbon source. The electrochemical growth of carbon nanostructures on substrates was...

Quantification of Model-Form Uncertainty in Drift-Diffusion Simulation Using Fractional Derivatives

2015 ◽  
Author(s):  
Yan Wang
Keyword(s):  
Diffusion Processes ◽  
Planck Equation ◽  
Optimization Procedure ◽  
Physical World ◽  
Drift Diffusion ◽  
Long Range Correlations ◽  
Modeling Process ◽  
Model Form ◽  
Generic Description ◽  
Non Gaussian

In modeling and simulation, model-form uncertainty arises from the lack of knowledge and simplification during modeling process and numerical treatment for ease of computation. Traditional uncertainty quantification approaches are based on assumptions of stochasticity in real, reciprocal, or functional spaces to make them computationally tractable. This makes the prediction of important quantities of interest such as rare events difficult. In this paper, a new approach to capture model-form uncertainty is proposed. It is based on fractional calculus, and its flexibility allows us to model a family of non-Gaussian processes, which provides a more generic description of the physical world. A generalized fractional Fokker-Planck equation (fFPE) is proposed to describe the drift-diffusion processes under long-range correlations and memory effects. A new model calibration approach based on the maximum accumulative mutual information is also proposed to reduce model-form uncertainty, where an optimization procedure is taken.

scholarly journals On Governance and the Demographic Transition

2012 ◽  
Vol 4 (6) ◽  
pp. 319-330
Author(s):  
Flaubert Mbiekop
Keyword(s):  
Demographic Transition ◽  
Financial Support ◽  
Overlapping Generations ◽  
The Other ◽  
Overlapping Generations Model ◽  
Child Quality ◽  
Mild Conditions ◽  
Weak Institutions ◽  
The One ◽  
Fertility Choices

It is now conventional wisdom that institutions shape household fertility choices, especially in developing countries. However, deeper insights into the mechanisms at play are still needed. This paper develops a game-theoretical framework with a simple overlapping-generations model to show how a typical household may come to prefer bearing and raising numerous children as a savings scheme for retirement and not rely on conventional outlets for saving when facing weak institutions. On the one hand weak institutions increase the risk that individuals may lose their savings if relying on conventional outlets. On the other hand, childbearing as an investment/savings scheme carries with it the risk that disguised or complete unemployment may prevent grown children from providing the expected old-age financial support. The typical household thus trades off between both types of risks, yet with more control in the latter case, as the likelihood of unemployment can be reduced by carefully selecting a child quality-quantity strategy. Mild conditions are sufficient to show that sound institutions induce less fertility and foster private saving and oldage consumption. A simple voting experiment unveils a tricky socio- economic dynamics whereby wealthier households may have stakes supporting weak institutions.

Efficient pseudo five-component synthesis of 4,4′-(arylmethylene)-bis(3-methyl-1-phenyl-1H-pyrazol-5-ol) derivatives promoted by a novel ionic liquid catalyst

2018 ◽  
Vol 73 (3-4) ◽  
pp. 191-195 ◽  
Author(s):  
Zahra Abshirini ◽  
Abdolkarim Zare
Keyword(s):  
Ionic Liquid ◽  
Disulfonic Acid ◽  
Thermal Gravimetric ◽  
One Pot ◽  
Mild Conditions ◽  
Acidic Ionic Liquid ◽  
Brønsted Acidic Ionic Liquid ◽  
The One ◽  
C Nmr

AbstractIn this research, initial production and characterization of a novel Brønsted-acidic ionic liquid, namely,N,N,N′,N′-tetramethylethylenediaminium-N,N′-disulfonic acid hydrogen sulfate ([TMEDSA][HSO4]2), has been described (characterization was achieved using Fourier-transform infrared spectroscopy,1H nuclear magnetic resonance (NMR),13C NMR, and mass and thermal gravimetric spectra). Thereafter, utilization of [TMEDSA][HSO4]2as a highly effectual catalyst for the synthesis of 4,4′-(arylmethylene)-bis(3-methyl-1-phenyl-1H-pyrazol-5-ol) derivatives through the one-pot pseudo five-component reaction of phenylhydrazine (2 eq.) with ethyl acetoacetate (2 eq.) and arylaldehydes (1 eq.) in relatively mild conditions, has been reported.

Study of Antioxidant Property of the Rhizome Extract of Polygonatum cirrhifolium (Mahameda) and its use in the green synthesis of Gold nanoparticles

2017 ◽  
Vol 1 (2) ◽  
Author(s):  
Braja Gopal Bag ◽  
Shib Shankar Dash ◽  
Anup Mandal
Keyword(s):  
Gold Nanoparticles ◽  
Green Synthesis ◽  
Room Temperature ◽  
Chemical Constituents ◽  
Antioxidant Property ◽  
Dpph Radical ◽  
Mild Conditions ◽  
One Step ◽  
The One

The antioxidant efficacy of the rhizome extract of Polygonatum cirrhifolium (Mahameda) has been studied against a stable 2, 2-diphenylpicrylhydrazyl (DPPH) radical at room temperature. The chemical constituents present in the rhizome extract have been utilized for the one step synthesis of stable gold nanoparticles at room temperature under very mild conditions.

On first passage times of sticky reflecting diffusion processes with double exponential jumps

2020 ◽  
Vol 57 (1) ◽  
pp. 221-236 ◽  
Author(s):  
Shiyu Song ◽  
Yongjin Wang
Keyword(s):  
Diffusion Processes ◽  
First Passage Time ◽  
Passage Time ◽  
Explicit Solutions ◽  
First Passage ◽  
Uhlenbeck Process ◽  
Double Exponential ◽  
Upper Level ◽  
First Passage Problem ◽  
Passage Times

AbstractWe explore the first passage problem for sticky reflecting diffusion processes with double exponential jumps. The joint Laplace transform of the first passage time to an upper level and the corresponding overshoot is studied. In particular, explicit solutions are presented when the diffusion part is driven by a drifted Brownian motion and by an Ornstein–Uhlenbeck process.

scholarly journals Limit theorems for hitting times of 1-dimensional generalized diffusions

1998 ◽  
Vol 152 ◽  
pp. 1-37
Author(s):  
Matsuyo Tomisaki ◽  
Makoto Yamazato
Keyword(s):  
Limit Theorems ◽  
Bessel Functions ◽  
Diffusion Processes ◽  
Hitting Times ◽  
Finite Dimensional ◽  
Independent Increments ◽  
Starting Point ◽  
Self Similar ◽  
The Mean ◽  
The One

Abstract.Limit theorems are obtained for suitably normalized hitting times of single points for 1-dimensional generalized diffusion processes as the hitting points tend to boundaries under an assumption which is slightly stronger than that the existence of limits γ + 1 of the ratio of the mean and the variance of the hitting time. Laplace transforms of limit distributions are modifications of Bessel functions. Results are classified by the one parameter {γ}, each of which is the degree of corresponding Bessel function. In case the limit distribution is degenerate to one point, by changing the normalization, we obtain convergence to the normal distribution. Regarding the starting point as a time parameter, we obtain convergence in finite dimensional distributions to self-similar processes with independent increments under slightly stronger assumption.

scholarly journals Limiting Distribution of the Present Value of a Portfolio

1994 ◽  
Vol 24 (1) ◽  
pp. 47-60 ◽  
Author(s):  
Gary Parker
Keyword(s):  
Interest Rates ◽  
Limiting Distribution ◽  
Present Value ◽  
Uhlenbeck Process ◽  
Insurance Contracts ◽  
Ornstein Uhlenbeck Process ◽  
Force Of Interest ◽  
The One

AbstractAn approximation of the distribution of the present value of the benefits of a portfolio of temporary insurance contracts is suggested for the case where the size of the portfolio tends to infinity. The model used is the one presented in Parker (1922b) and involves random interest rates and future lifetimes. Some justifications of the approximation are given. Illustrations for limiting portfolios of temporary insurance contracts are presented for an assumed Ornstein-Uhlenbeck process for the force of interest.

Sign in / Sign up

Export Citation Format

Share Document