Calculation of Transition Probabilities of SDEs Only from the Knowledge of Marginal Probabilities Using the CDF-Equivalent Brownian Motion Method

2018 ◽  
Author(s):  
Ahsan Amin
Keyword(s):  
Brownian Motion ◽  
Transition Probabilities ◽  
Motion Method

Surface Simulation Algorithm Streamlining by the Brownian Motion Method on the Criterion of Iterations Number Minimizing

2017 ◽  
Vol 5 (1) ◽  
pp. 43-50 ◽  
Author(s):  
Брылкин ◽  
Yuriy Brylkin
Keyword(s):  
Brownian Motion ◽  
Fractal Dimension ◽  
Geometric Model ◽  
Navier Stokes ◽  
Space Forms ◽  
High Enthalpy ◽  
Fractal Surfaces ◽  
Torus Knot ◽  
Necessary And Sufficient ◽  
Motion Method

The paper has been devoted to construction of geometric model for real surface’s compartment at micro- and nanoscales with known fractal dimension. Receiving data on the real surface’s fractal dimension has been considered in [8; 9; 11; 13; 20]. Fractal dimension as a relief development measure has been accepted for the necessary and sufficient condition of the model construction. As is known, for a flying vehicle’s appearance the comprehensive characteristics research is performed with ground work in aerodynamic tubes, and numerical simulation. Similarly, a fragment of product’s heat protection is tested in high-enthalpy facilities for research of physico-chemical processes in the boundary layer, as well as for confirmation of calculations of interactions between rarefied gas’s particles and the surface. In this work has been performed the analysis of geometrical interpretations of algorithms for the fractal surfaces formation based on the Brownian motion method, proposed to use in calculations by Monte Carlo and Navier-Stokes methods. A point choice leading to construction of secant or tangent planes to space forms has been assigned as an element of randomness per iteration. All proposed algorithms lead to construction of surfaces with fractal dimension D ≈ 2.5, but by different iterations number. A tendency to reduce the iterations number required to achieve a specific fractal dimension by increasing the capacity of many lines for plane compartment digitalization has been revealed. The best result has been obtained by construction of projections for section of surface called a torus knot [19, 22]. Visualization was carried out in ASCON Kompas 3Dv.14 program on algorithms results in MathCAD environment.

scholarly journals Diffusion and the Brownian motion

1949 ◽  
Vol 198 (1052) ◽  
pp. 94-116 ◽  
Keyword(s):  
Brownian Motion ◽  
Free Path ◽  
Transition Probabilities ◽  
The Other ◽  
Approximate Theory ◽  
Gaseous Diffusion ◽  
Self Diffusion ◽  
Second Moments ◽  
Diffusion In Liquids ◽  
The One

In the present paper the phenomenon of diffusion is examined in the light of the theory of the Brownian motion. The coefficients of self-diffusion, ordinary diffusion and thermal diffusion are expressed in terms of the first and second moments of certain transition probabilities familiar in the theory of the Brownian motion. It is then found possible in gases of low or moderate density where a fairly well-defined free path exists to follow the future course of a given molecule statistically to as many free flights as required provided the velocity distribution of the molecules in the medium is known. This consideration on the one hand leads to a rigorous expression for the coefficient of self-diffusion directly calculated from a Maxwellian distribution, and on the other serves to clarify the relation between the old free-path theory of gaseous diffusion and the rigorous theory of gaseous diffusion and between self-diffusion and mutual diffusion. Further, an approximate theory of diffusion in liquids corresponding to the old free-path theory in gases is suggested.

scholarly journals APPROXIMATION METHODS FOR INHOMOGENEOUS GEOMETRIC BROWNIAN MOTION

2019 ◽  
Vol 22 (02) ◽  
pp. 1850055
Author(s):  
LUCA CAPRIOTTI ◽  
YUPENG JIANG ◽  
GAUKHAR SHAIMERDENOVA
Keyword(s):  
Brownian Motion ◽  
Power Series ◽  
Interest Rates ◽  
High Precision ◽  
Transition Probabilities ◽  
Geometric Brownian Motion ◽  
Approximation Methods ◽  
Time Horizons

We present an accurate and easy-to-compute approximation of the transition probabilities and the associated Arrow-Debreu (AD) prices for the inhomogeneous geometric Brownian motion (IGBM) model for interest rates, default intensities or volatilities. Through this procedure, dubbed exponent expansion, transition probabilities and AD prices are obtained as a power series in time to maturity. This provides remarkably accurate results — for time horizons up to several years — even when truncated after the first few terms. For farther time horizons, the exponent expansion can be combined with a fast numerical convolution to obtain high-precision results.

Generation of non-Kolmogorov atmospheric turbulence phase screen using intrinsic embedding fractional Brownian motion method

Optik ◽  
2020 ◽  
Vol 207 ◽  
pp. 164444
Author(s):  
Kaidi Wang ◽  
Xiuqin Su ◽  
Zhe Li ◽  
Shaobo Wu ◽  
Wei Zhou ◽  
...  
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Atmospheric Turbulence ◽  
Phase Screen ◽  
Motion Method

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

Brownian motion with quadratic killing and some implications

1986 ◽  
Vol 23 (04) ◽  
pp. 893-903 ◽  
Author(s):  
Michael L. Wenocur
Keyword(s):  
Brownian Motion ◽  
Weibull Distribution ◽  
Special Function ◽  
Function Theory ◽  
Killing Rate

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.

EELS white line intensities calculated for the 3d and 4d metals

1989 ◽  
Vol 47 ◽  
pp. 388-389
Author(s):  
C. C. Ahn ◽  
D. H. Pearson ◽  
P. Rez ◽  
B. Fultz
Keyword(s):  
Experimental Data ◽  
Line Intensity ◽  
Transition Probabilities ◽  
Initial Increase ◽  
White Line ◽  
Hartree Fock ◽  
Line Intensities ◽  
Integrated Intensity ◽  
X Ray Absorption ◽  
The Continuum

Previous experimental measurements of the total white line intensities from L2,3 energy loss spectra of 3d transition metals reported a linear dependence of the white line intensity on 3d occupancy. These results are inconsistent, however, with behavior inferred from relativistic one electron Dirac-Fock calculations, which show an initial increase followed by a decrease of total white line intensity across the 3d series. This inconsistency with experimental data is especially puzzling in light of work by Thole, et al., which successfully calculates x-ray absorption spectra of the lanthanide M4,5 white lines by employing a less rigorous Hartree-Fock calculation with relativistic corrections based on the work of Cowan. When restricted to transitions allowed by dipole selection rules, the calculated spectra of the lanthanide M4,5 white lines show a decreasing intensity as a function of Z that was consistent with the available experimental data.Here we report the results of Dirac-Fock calculations of the L2,3 white lines of the 3d and 4d elements, and compare the results to the experimental work of Pearson et al. In a previous study, similar calculations helped to account for the non-statistical behavior of L3/L2 ratios of the 3d metals. We assumed that all metals had a single 4s electron. Because these calculations provide absolute transition probabilities, to compare the calculated white line intensities to the experimental data, we normalized the calculated intensities to the intensity of the continuum above the L3 edges. The continuum intensity was obtained by Hartree-Slater calculations, and the normalization factor for the white line intensities was the integrated intensity in an energy window of fixed width and position above the L3 edge of each element.

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