scholarly journals A Necessary Characteristic Equation of Diffusion Processes Having Gaussian Marginals

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Syeda Rabab Mudakkar
Keyword(s):  
Fourier Transform ◽  
Diffusion Process ◽  
Characteristic Equation ◽  
Diffusion Coefficients ◽  
Diffusion Processes ◽  
Kolmogorov Equation ◽  
Marginal Density ◽  
Operator Approach ◽  
One Dimensional ◽  
And Diffusion

The aim of this work is to characterize one-dimensional homogeneous diffusion process, under the assumption that marginal density of the process is Gaussian. The method considers the forward Kolmogorov equation and Fourier transform operator approach. The result establishes the necessary characteristic equation between drift and diffusion coefficients for homogeneous and nonhomogeneous diffusion processes. The equation for homogeneous diffusion process leads to characterize the possible diffusion processes that can exist. Two well-known examples using the necessary characteristic equation are also given.

On the threshold strategies in optimal stopping problems for diffusion processes

2017 ◽  
Vol 54 (3) ◽  
pp. 963-969 ◽  
Author(s):  
Vadim Arkin ◽  
Alexander Slastnikov
Keyword(s):  
Diffusion Process ◽  
Optimal Stopping ◽  
Diffusion Processes ◽  
Sufficient Conditions ◽  
Payoff Function ◽  
Threshold Strategy ◽  
One Dimensional ◽  
Stopping Set ◽  
Optimal Stopping Problems ◽  
Necessary And Sufficient

Abstract We study a problem when the optimal stopping for a one-dimensional diffusion process is generated by a threshold strategy. Namely, we give necessary and sufficient conditions (on the diffusion process and the payoff function) under which a stopping set has a threshold structure.

Sojourns and extremes of a diffusion process on a fixed interval

1982 ◽  
Vol 14 (4) ◽  
pp. 811-832 ◽  
Author(s):  
Simeon M. Berman
Keyword(s):  
Diffusion Process ◽  
Lebesgue Measure ◽  
Stationary Distribution ◽  
Real Line ◽  
Diffusion Coefficients ◽  
Limit Theorems ◽  
Random Variable ◽  
Fixed Interval ◽  
The Real ◽  
And Diffusion

Let X(t), , be an Ito diffusion process on the real line. For u > 0 and t > 0, let Lt(u) be the Lebesgue measure of the set . Limit theorems are obtained for (i) the distribution of Lt(u) for u → ∞and fixed t, and (ii) the tail of the distribution of the random variable max[0, t]X(s). The conditions on the process are stated in terms of the drift and diffusion coefficients. These conditions imply the existence of a stationary distribution for the process.

Estimation for discretely observed diffusions using transform functions

2004 ◽  
Vol 41 (A) ◽  
pp. 99-118 ◽  
Author(s):  
Leah Kelly ◽  
Eckhard Platen ◽  
Michael Sørensen
Keyword(s):  
Asymptotic Normality ◽  
Diffusion Coefficients ◽  
Diffusion Processes ◽  
Estimation Technique ◽  
Consistency And Asymptotic Normality ◽  
And Diffusion ◽  
Explicit Estimators

This paper introduces a new estimation technique for discretely observed diffusion processes. Transform functions are applied to transform the data to obtain good and easily calculated estimators of both the drift and diffusion coefficients. Consistency and asymptotic normality of the resulting estimators is investigated. Power transforms are used to estimate the parameters of affine diffusions, for which explicit estimators are obtained.

scholarly journals Empirical and Theoretical Characterization of the Diffusion Process of Different Gadolinium-Based Nanoparticles within the Brain Tissue after Ultrasound-Induced Permeabilization of the Blood-Brain Barrier

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Allegra Conti ◽  
Rémi Magnin ◽  
Matthieu Gerstenmayer ◽  
Nicolas Tsapis ◽  
Erik Dumont ◽  
...  
Keyword(s):  
Diffusion Process ◽  
Brain Tissue ◽  
Blood Brain Barrier ◽  
Diffusion Coefficients ◽  
Brain Barrier ◽  
Apparent Diffusion Coefficients ◽  
Blood Brain ◽  
The Brain ◽  
And Diffusion

Low-intensity focused ultrasound (FUS), combined with microbubbles, is able to locally, and noninvasively, open the blood-brain barrier (BBB), allowing nanoparticles to enter the brain. We present here a study on the diffusion process of gadolinium-based MRI contrast agents within the brain extracellular space after ultrasound-induced BBB permeabilization. Three compounds were tested (MultiHance, Gadovist, and Dotarem). We characterized their diffusion through in vivo experimental tests supported by theoretical models. Specifically, by estimation of the free diffusion coefficients from in vitro studies and of apparent diffusion coefficients from in vivo experiments, we have assessed tortuosity in the right striatum of 9 Sprague Dawley rats through a model correctly describing both vascular permeability as a function of time and diffusion processes occurring in the brain tissue. This model takes into account acoustic pressure, particle size, blood pharmacokinetics, and diffusion rates. Our model is able to fully predict the result of a FUS-induced BBB opening experiment at long space and time scales. Recovered values of tortuosity are in agreement with the literature and demonstrate that our improved model allows us to assess that the chosen permeabilization protocol preserves the integrity of the brain tissue.

Approximation of Euler–Maruyama for one-dimensional stochastic differential equations involving the maximum process

2020 ◽  
Vol 26 (1) ◽  
pp. 33-47
Author(s):  
Kamal Hiderah
Keyword(s):  
Differential Equations ◽  
Strong Convergence ◽  
Stochastic Differential Equations ◽  
Diffusion Coefficients ◽  
One Dimensional ◽  
Maximum Process ◽  
And Diffusion

AbstractThe aim of this paper is to show the approximation of Euler–Maruyama {X_{t}^{n}} for one-dimensional stochastic differential equations involving the maximum process. In addition to that it proves the strong convergence of the Euler–Maruyama whose both drift and diffusion coefficients are Lipschitz. After that, it generalizes to the non-Lipschitz case.

FORECASTING GAS EXCHANGE DYNAMICS OF GOBS WITH MINING AIR AND SURFACE LAYER OF ATMOSPHERE

2020 ◽  
Vol 3 (1) ◽  
pp. 253-262
Author(s):  
A.N. KACHURIN ◽  
◽  
O.A. AFANASIEV ◽  
D.N. SHKURATCKYI ◽  
◽  
...  
Keyword(s):  
Carbon Dioxide ◽  
Surface Layer ◽  
Gas Exchange ◽  
Atmospheric Pressure ◽  
Diffusion Processes ◽  
Diffusion Mode ◽  
Diffusion Flow ◽  
Coal Seams ◽  
One Dimensional ◽  
And Diffusion

It is noted that filtration and diffusion processes in coal seams, worked-out spaces and workings of carbon dioxide mines are satisfactorily described by parabolic filtration equations for one-dimensional semi-infinite space. Linearization of the equations of filtration gas transport allows obtaining analytical solutions for a wide class of applied problems. A model has been developed for the movement of dead air through underworked rocks from mined-out areas to the earth's surface for the conditions of the Eastern Donbass and Kuzbass. At a stable atmospheric pressure, gas exchange occurs in a diffusion mode. The dependence of the diffusion flow of gases from the worked-out space to the earth's surface is obtained. Dependencies for the forecast of methane release on the earth's surface of allotments of the liquidated mines of Kuz-Bass are obtained.

Correlated photoluminescence spectroscopy investigation of grain boundaries and diffusion processes in nanocrystalline and amorphous silicon (nc-Si:H) mixtures

2011 ◽  
Vol 1321 ◽  
Author(s):  
Jeremy D. Fields ◽  
K. G. Kiriluk ◽  
D. C. Bobela ◽  
L. Gedvilas ◽  
P. C. Taylor
Keyword(s):  
Fourier Transform ◽  
Thermal Annealing ◽  
Diffusion Processes ◽  
Volume Fraction ◽  
Nanocrystalline Silicon ◽  
Silicon Alloys ◽  
Thermally Driven ◽  
Grain Boundary Characteristics ◽  
Boundary Characteristics ◽  
And Diffusion

ABSTRACTPhotoluminescence (PL) spectra obtained with correlated set of experiments investigating grain boundary characteristics and diffusion processes in nanocrystalline silicon alloys (nc-Si:H), provide insight regarding formation and passivation of electronic defects in these regions. Based upon current results and previous works we believe thermally driven processes induce a PL band centered at 0.7 eV upon thermal annealing, and most likely involve diffusion of hydrogen and oxygen near interfaces. A nc-Si:H sample set with varied crystal volume fraction, Xc, was subject to thermal annealing treatments at different temperatures – each exceeding the deposition temperature. Fourier-transform photoluminescence (FTPL) and Fourier-transform infrared absorption spectroscopy (FTIR), were employed to correlate the relative 0.7 eV defect band emergence with compositional changes indicative of Si–Hx and Si–O species, for each sample, at each temperature, respectively. Hydrogen effusion data provide additional perspective.We find the Xc to strongly affect susceptibility of nc-Si:H to oxygen related effects. The higher the Xc, the more readily oxygen penetrates the nc-Si:H network. We attribute this relationship to elevated diffusivity of oxygen in highly crystalline nc-Si:H materials, owing to their abundance of gain boundaries and interfaces, which serve as pathways for impurity migration. These findings corroborate the expectation that oxygen impurities and diffusion processes contribute to development of microstructural features giving rise to radiative recombination through deep defects in nc-Si:H.

DIFFUSION IN THE FRENKEL–KONTOROVA MODEL WITH ANHARMONIC INTERATOMIC INTERACTIONS

1994 ◽  
Vol 08 (17) ◽  
pp. 2353-2389 ◽  
Author(s):  
OLEG M. BRAUN ◽  
IRINA I. ZELENSKAYA ◽  
YURI S. KIVSHAR
Keyword(s):  
Low Temperature ◽  
Diffusion Coefficients ◽  
Type Equation ◽  
Chemical Diffusion ◽  
Phenomenological Approach ◽  
Superionic Conductors ◽  
One Dimensional ◽  
Anisotropic Layers ◽  
And Diffusion ◽  
Kontorova Model

Low-temperature diffusion and transport properties of the generalized Frenkel–Kontorova model are investigated analytically in the framework of a phenomenological approach which treats a system of strongly interacting atoms as a system of weaklyinteracting quasiparticles (kinks). The model takes into account realistic (anharmonic) interaction of particles subjected into a periodic substrate potential, and such a generalization leads to a series of novel effects which we expect are related to the experimentally-observed phenomena in several quasi-one-dimensional systems. Analysing the concentration dependences in the framework of the kink phenomenology, we use the renormalization procedure when the atomic structure with a complex unit cell is treated as (more simple) periodic structure of kinks. Using phenomenology of the ideal kink gas, the low-temperature states of the chain are described as those consisting of "residual" kinks supplemented by thermally-excited kinks. This approach allows us to describe the ground states of the chain as a hierarchy of "melted" kink lattices. Dynamical and diffusion properties of the system are then described in terms of the kink dynamics and kink diffusion. The motion equation for a single kink is reduced to a Langevin-type equation which is investigated with the help of the Kramers theory. Susceptibility, conductivity, self-diffusion and chemical diffusion coefficients of the chain are calculated as functions of the kink diffusion coefficient. In this way, we qualitatively analyze, for the first time to our knowledge, dependence of the different diffusion coefficients on the concentration of atoms in the chain. The results are applied to describe peculiarities in conductivity and diffusion coefficients of quasi-one-dimensional systems, in particular, superionic conductors and anisotropic layers of atoms adsorbed on crystal surfaces which were earlier investigated experimentally.

First-Passage Problems for Asymmetric Diffusions and Skew-diffusion Processes

2009 ◽  
Vol 16 (04) ◽  
pp. 325-350 ◽  
Author(s):  
Mario Abundo
Keyword(s):  
Diffusion Process ◽  
Diffusion Processes ◽  
Exit Time ◽  
Skew Brownian Motion ◽  
One Dimensional ◽  
Mean Exit Time ◽  
The Mean ◽  
The Right ◽  
Analytical Expressions ◽  
Skew Diffusion

For a, b > 0, we consider a temporally homogeneous, one-dimensional diffusion process X(t) defined over I = (-b, a), with infinitesimal parameters depending on the sign of X(t). We suppose that, when X(t) reaches the position 0, it is reflected rightward to δ with probability p > 0 and leftward to -δ with probability 1 - p, where δ > 0. Closed analytical expressions are found for the mean exit time from the interval (-b, a), and for the probability of exit through the right end a, in the limit δ → 0+, generalizing the results of Lefebvre, holding for asymmetric Wiener process. Moreover, in alternative to the heavy analytical calculations, a numerical method is presented to estimate approximately the quantities above. Furthermore, on the analogy of skew Brownian motion, the notion of skew diffusion process is introduced. Some examples and numerical results are also reported.

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