Orthogonal Polynomials in the Spectral Analysis of Markov Processes

2021 ◽  
Author(s):  
Manuel Domínguez de la Iglesia
Keyword(s):  
Stochastic Processes ◽  
Orthogonal Polynomials ◽  
Markov Processes ◽  
Diffusion Processes ◽  
Special Functions ◽  
Extensive Literature ◽  
Associated Operators ◽  
And Diffusion ◽  
Selection Of ◽  
Birth Death

In pioneering work in the 1950s, S. Karlin and J. McGregor showed that probabilistic aspects of certain Markov processes can be studied by analyzing orthogonal eigenfunctions of associated operators. In the decades since, many authors have extended and deepened this surprising connection between orthogonal polynomials and stochastic processes. This book gives a comprehensive analysis of the spectral representation of the most important one-dimensional Markov processes, namely discrete-time birth-death chains, birth-death processes and diffusion processes. It brings together the main results from the extensive literature on the topic with detailed examples and applications. Also featuring an introduction to the basic theory of orthogonal polynomials and a selection of exercises at the end of each chapter, it is suitable for graduate students with a solid background in stochastic processes as well as researchers in orthogonal polynomials and special functions who want to learn about applications of their work to probability.

Meridional Circulation, Turbulence, and Diffusion Processes in Stars

1976 ◽  
Vol 32 ◽  
pp. 109-116 ◽  
Author(s):  
S. Vauclair
Keyword(s):  
Convection Zone ◽  
Diffusion Processes ◽  
Meridional Circulation ◽  
Diffusion Time ◽  
Work In Progress ◽  
First Results ◽  
Stellar Envelopes ◽  
And Diffusion ◽  
Turbulence And Diffusion ◽  
Hr Diagram

This paper gives the first results of a work in progress, in collaboration with G. Michaud and G. Vauclair. It is a first attempt to compute the effects of meridional circulation and turbulence on diffusion processes in stellar envelopes. Computations have been made for a 2 Mʘstar, which lies in the Am - δ Scuti region of the HR diagram.Let us recall that in Am stars diffusion cannot occur between the two outer convection zones, contrary to what was assumed by Watson (1970, 1971) and Smith (1971), since they are linked by overshooting (Latour, 1972; Toomre et al., 1975). But diffusion may occur at the bottom of the second convection zone. According to Vauclair et al. (1974), the second convection zone, due to He II ionization, disappears after a time equal to the helium diffusion time, and then diffusion may happen at the bottom of the first convection zone, so that the arguments by Watson and Smith are preserved.

NMR-Study of Structure and Diffusion Processes in Li3N

1980 ◽  
Vol 41 (C6) ◽  
pp. C6-28-C6-31 ◽  
Author(s):  
R. Messer ◽  
H. Birli ◽  
K. Differt
Keyword(s):  
Diffusion Processes ◽  
Nmr Study ◽  
And Diffusion

Effect of cluster-gradient architecture of nanostructured topocomposites on features of tribointeraction with heterophased material

2020 ◽  
pp. 130-135
Author(s):  
D.N. Korotaev ◽  
K.N. Poleshchenko ◽  
E.N. Eremin ◽  
E.E. Tarasov
Keyword(s):  
Wear Resistance ◽  
Titanium Alloy ◽  
Energy Dissipation ◽  
Phase Structure ◽  
Diffusion Processes ◽  
Structural Phase ◽  
High Wear Resistance ◽  
Wear Characteristics ◽  
And Diffusion

The wear resistance and wear characteristics of cluster-gradient architecture (CGA) nanostructured topocomposites are studied. The specifics of tribocontact interaction under microcutting conditions is considered. The reasons for retention of high wear resistance of this class of nanostructured topocomposites are studied. The mechanisms of energy dissipation from the tribocontact zone, due to the nanogeometry and the structural-phase structure of CGA topocomposites are analyzed. The role of triboactivated deformation and diffusion processes in providing increased wear resistance of carbide-based topocomposites is shown. They are tested under the conditions of blade processing of heat-resistant titanium alloy.

Certain Problems with the Application of Stochastic Diffusion Processes for the Description of Chemical Engineering Phenomena. Diffusional Change of Solid Particle Size

1996 ◽  
Vol 61 (4) ◽  
pp. 536-563
Author(s):  
Vladimír Kudrna ◽  
Pavel Hasal
Keyword(s):  
Particle Size ◽  
Solid Particle ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Granular Systems ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Diffusion Term ◽  
Population Balances ◽  
And Diffusion

To the description of changes of solid particle size in population, the application was proposed of stochastic differential equations and diffusion equations adequate to them making it possible to express the development of these populations in time. Particular relations were derived for some particle size distributions in flow and batch equipments. It was shown that it is expedient to complement the population balances often used for the description of granular systems by a "diffusion" term making it possible to express the effects of random influences in the growth process and/or particle diminution.

scholarly journals Non-local Solvable Birth–Death Processes

2021 ◽  
Author(s):  
Giacomo Ascione ◽  
Nikolai Leonenko ◽  
Enrica Pirozzi
Keyword(s):  
Differential Equations ◽  
Orthogonal Polynomials ◽  
Limit Distribution ◽  
Spectral Decomposition ◽  
Strong Solutions ◽  
Stochastic Representation ◽  
Discrete Approximations ◽  
Local Difference ◽  
Non Local ◽  
Birth Death

AbstractIn this paper, we study strong solutions of some non-local difference–differential equations linked to a class of birth–death processes arising as discrete approximations of Pearson diffusions by means of a spectral decomposition in terms of orthogonal polynomials and eigenfunctions of some non-local derivatives. Moreover, we give a stochastic representation of such solutions in terms of time-changed birth–death processes and study their invariant and their limit distribution. Finally, we describe the correlation structure of the aforementioned time-changed birth–death processes.

scholarly journals Influence of Geometry on Thin Layer and Diffusion Processes at Carbon Electrodes

Langmuir ◽  
2021 ◽  
Author(s):  
Qun Cao ◽  
Zijun Shao ◽  
Dale K. Hensley ◽  
Nickolay V. Lavrik ◽  
B. Jill Venton
Keyword(s):  
Thin Layer ◽  
Diffusion Processes ◽  
Carbon Electrodes ◽  
And Diffusion

scholarly journals All adapted topologies are equal

2020 ◽  
Vol 178 (3-4) ◽  
pp. 1125-1172
Author(s):  
Julio Backhoff-Veraguas ◽  
Daniel Bartl ◽  
Mathias Beiglböck ◽  
Manu Eder
Keyword(s):  
Stochastic Processes ◽  
Weak Topology ◽  
Equilibrium Problems ◽  
Diffusion Processes ◽  
Temporal Structure ◽  
Wasserstein Distance ◽  
Optimal Stopping Problems ◽  
Reward Functions ◽  
Nested Distance ◽  
The Stability

Abstract A number of researchers have introduced topological structures on the set of laws of stochastic processes. A unifying goal of these authors is to strengthen the usual weak topology in order to adequately capture the temporal structure of stochastic processes. Aldous defines an extended weak topology based on the weak convergence of prediction processes. In the economic literature, Hellwig introduced the information topology to study the stability of equilibrium problems. Bion–Nadal and Talay introduce a version of the Wasserstein distance between the laws of diffusion processes. Pflug and Pichler consider the nested distance (and the weak nested topology) to obtain continuity of stochastic multistage programming problems. These distances can be seen as a symmetrization of Lassalle’s causal transport problem, but there are also further natural ways to derive a topology from causal transport. Our main result is that all of these seemingly independent approaches define the same topology in finite discrete time. Moreover we show that this ‘weak adapted topology’ is characterized as the coarsest topology that guarantees continuity of optimal stopping problems for continuous bounded reward functions.

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