A general class of models for stationary two-dimensional random processes

Biometrika ◽  
1985 ◽  
Vol 72 (2) ◽  
pp. 281-291 ◽  
Author(s):  
A. V. VECCHIA
Keyword(s):  
General Class ◽  
Random Processes ◽  
Two Dimensional

ON SUPERSYMMETRIC NONLINEAR σ MODELS AND CLASSICAL DYNAMICAL SYSTEMS

1996 ◽  
Vol 11 (06) ◽  
pp. 1101-1115
Author(s):  
ANTTI J. NIEMI ◽  
KAUPO PALO
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Partition Function ◽  
Integrable Systems ◽  
Morse Theory ◽  
General Class ◽  
Loop Space ◽  
Two Dimensional ◽  
Hamiltonian Flow ◽  
Classical Dynamical System

We construct a two-dimensional nonlinear σ model that describes the Hamiltonian flow in the loop space of a classical dynamical system. This model is obtained by equivariantizing the standard N=1 supersymmetric nonlinear σ model by the Hamiltonian flow. We use localization methods to evaluate the corresponding partition function for a general class of integrable systems, and find relations that can be viewed as generalizations of standard relations in classical Morse theory.

scholarly journals ON APPROXIMATION OF VALUE FUNCTIONS FOR CONTROLLED DISCONTINUOUS RANDOM PROCESSES

2011 ◽  
Vol 16 (1) ◽  
pp. 260-272
Author(s):  
Svetlana Danilenko ◽  
Henrikas Pragarauskas
Keyword(s):  
Rate Of Convergence ◽  
General Class ◽  
Diffusion Processes ◽  
Random Processes ◽  
Value Functions ◽  
Control Policies ◽  
Controlled Processes ◽  
Constant Control

We consider the problem of approximation of value functions for controlled possibly degenerated diffusion processes with jumps by using piece-wise constant control policies. A rate of convergence for the corresponding value functions is established provided that the coefficients of controlled processes are sufficiently smooth. The paper extends the results of N.V. Krylov to a more general class of controlled processes.

Compact Probabilistic Representation of Random Processes

1982 ◽  
Vol 49 (4) ◽  
pp. 871-876 ◽  
Author(s):  
S. F. Masri ◽  
R. K. Miller
Keyword(s):  
Random Vibration ◽  
Random Processes ◽  
System Response ◽  
Two Dimensional ◽  
Probabilistic Representation ◽  
Simple Analytical Expression ◽  
Orthogonal Functions ◽  
Covariance Kernel ◽  
Transmission Properties ◽  
Transmission Studies

A method is given for representing analytically defined or data-based covariance kernels of arbitrary random processes in a compact form that results in simplified, analytical, random-vibration transmission studies. The method uses two-dimensional orthogonal functions to represent the covariance kernel of the underlying random process. Such a representation leads to a relatively simple analytical expression for the covariance kernel of the linear system response which consists of two independent groups of terms: one reflecting the input characteristics, and the other accounting for the transmission properties of the excited dynamic system. The utility of the method is demonstrated by application to a covariance kernel widely used in random-vibration studies.

scholarly journals The five-point non-coherent model of a distributed radar object providing the independent control of angle noise probability characteristics along two orthogonal coordinate axes

2021 ◽  
Vol 2134 (1) ◽  
pp. 012003
Author(s):  
A O Podkopayev ◽  
M A Stepanov
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Random Processes ◽  
Radar Target ◽  
Two Dimensional ◽  
Independent Control ◽  
Noise Parameters ◽  
Fixed Model

Abstract The two-dimensional five-point non-coherent model replacing a distributed radar target is explored in this work. Four fixed model points are set in corners of the square but the fifth movable point lies inside of this square. Model points are supplied by normal uncorrelated random processes. The possibilities of the five-point non-coherent model of a distributed radar object for independent control of the producing angle noise parameters along two orthogonal coordinate axes are explored. The disadvantage of this model is noted - the connection of parameters values of angle noise probability density function for two coordinate axes. The expression describing this connection is specified. Expressions determining the boundaries of the allowable coordinate values of the fifth movable point of the five-point non-coherent model, within which the model provides the set parameters of the angle noise probability density function, are defined. The arrived results are validated by program simulations.

APPLICATIONS OF GREEN’S THEOREM IN TWO‐DIMENSIONAL FILTERING

Geophysics ◽  
1967 ◽  
Vol 32 (4) ◽  
pp. 739-740 ◽  
Author(s):  
Wayne T. Ford
Keyword(s):  
General Class ◽  
Present Note ◽  
Two Dimensional ◽  
Double Integral ◽  
Considerable Effort ◽  
Green's Theorem ◽  
Green’S Theorem ◽  
Special Cases ◽  
Two Dimensional Filtering ◽  
Band Pass

There seems to be considerable interest in the design of a discrete two‐dimensional filter from band‐pass and band‐reject area specification in the ω‐k plane. The calculation of such a filter requires the evaluation of a double integral for each filter point. Considerable effort has been expended in efforts to give the results of these integrations in closed form for special cases. The present note was written to point out that a rather general class of filters can be calculated from a single computer program. The simplicity of this program is a result of an elementary application of Green’s Theorem in the plane.

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