| An Analysis of Methods for Extracting Aerodynamic Coefficients from Test Data. |
FEB 1973 |
148 pages |
| Authors:
Donald C. Daniel; FLORIDA UNIV GAINESVILLE
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 | An analysis of numerical methods for extracting aerodynamic coefficients from dynamic test data has been conducted. The emphasis of the analysis is on the effects that random measurement errors in the data and random disturbances in the system have on the accuracy with which the coefficients for linear and nonlinear systems can be determined. Both deterministic and stochastic methods for extracting the coefficients and determining their uncertainties are considered. The ... |
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| A POPULATION PROCESS WITH MARKOVIAN PROGENIES. |
18 AUG 1969 |
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| Authors:
Peter J. Brockwell; Joseph M. Gani; STANFORD UNIV CALIF DEPT OF STATISTICS; STANFORD UNIV CALIF DEPT OF STATISTICS
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 | A population is considered in which the number of individuals X sub t, t = 0, 1, 2, ..., added to the population in the time interval (t, t+1) is a Markov chain with the non-negative integers as state-space. At the end of each interval one individual is removed from the population, the process coming to a stop when the population size is zero. A method is developed ... |
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| DYNAMIC EFFECTS ON ELASTIC SYSTEMS. |
08 AUG 1969 |
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| Authors:
George H. Handelman; William E. Boyce; RENSSELAER POLYTECHNIC INST TROY N Y DEPT OF MATHEMATICS; RENSSELAER POLYTECHNIC INST TROY N Y DEPT OF MATHEMATICS
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| The paper is the final report for the project, Dynamic Effects on Elastic Systems. The mathematical efforts have followed two major directions: (1) the study of stochastic problems in differential equations and (2) wave-motion and vibration problems in acoustic and elastic media. (Author) |
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| ON MARKOVIAN LATTICES, |
28 JUL 1969 |
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| Authors:
N. Thomas Gaarder; HAWAII UNIV HONOLULU INFORMATION SCIENCES PROGRAM; HAWAII UNIV HONOLULU INFORMATION SCIENCES PROGRAM
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| In many information processing problems one is confronted with modeling a random quantity that depends upon two, or more, parameters. A natural model for such a quantity is a random function of multi-dimensional argument; i.e., a random field. In this paper we consider random fields that are defined on only a discrete set of points; the points from a rectangular lattice in an n-dimensional space. The Markovian ... |
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| Random Measures. |
JUN 1969 |
50 pages |
| Authors:
Michael G. Fahey; AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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| A random measure may be thought of as a random set function which is almost surely a measure. Some results obtained by Ryll-Nardzewski for point processes on the real line are extended and the Laplace functional is introduced. Completely random measures, infinitely divisible random measures, and stationary random measures are characterized. Homogeneous random measures are introduced with examples and interpretations. A general characterization theorem for homogeneous random measures is proved. ... |
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| A Decision Theoretic Approach to the Stochastic Approximation of the Root of an Unknown Function. |
JUN 1969 |
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| Authors:
Robert M. Emmerichs; AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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| A decision theoretic approach is used to characterize stochastic approximation procedures. The basic foundation of stochastic approximation and statistical decision theory is presented. These two fields are combined using the restrictive problem of estimating the unknown root of a linear function with unit slope. The restrictions on the function are relaxed, and convergence almost surely is demonstrated in the general case. A section on applications of stochastic approximation in fields ... |
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| STOCHASTIC ORDINARY DIFFERENTIAL EQUATIONS. |
OCT 1967 |
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| Authors:
John L. Strand; CALIFORNIA UNIV BERKELEY DEPT OF MATHEMATICS
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| If some of the driving forces or coefficients which occur in the differential equation are replaced by random functions (i.e. stochastic processes) one has a random differential equation. Basic existence theorems are established for these based on the different interpretations which may then be attached to the notion of derivative, assumptions on the equations, and types of solutions. A new class of generalized stochastic function is introduced. |
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| RESEARCH ON SPECTRAL ANALYSIS. |
22 MAR 1967 |
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| Authors:
N. R. Goodman; M. R. Dubman; ROCKETDYNE CANOGA PARK CALIF
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| The report presents abstracts of three technical reports entitled 'Statistical Tests for Stationarity Within the Framework of Harmonizable Time Series', 'The Spectral Characterization and Comparison of Nonstationary Processes', and 'Theory of Time-Varying Spectral Estimates'. (Author) |
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| ON A NONHOMOGENEOUS RANDOM DIFFUSION EQUATION. |
JAN 1967 |
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| Authors:
Edmund H. Inselmann; FRANKFORD ARSENAL PHILADELPHIA PA PITMAN-DUNN RESEARCH LABS
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| This paper deals with the solution of random diffusion equations. The solution is obtained by using eigenfunction methods. The mean and all the correlation functions are computed. |
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| AN INVESTIGATION INTO THE ENSEMBLE PROPERTIES OF A WIENER CANONICAL EXPANSION. |
29 JUL 1966 |
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| Authors:
Joel Owen; Henry Kashian; DONALD B. BRICK; INFORMATION RESEARCH ASSOCIATES INC LEXINGTON MA
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| In this paper consideration is given to an orthogonal expansion of functionals of a stochastic process x(t). Derived is the explicit evaluation of the b sub k1 for a class of processes x(t). The class considered is the class k sub m of differential process whose differential elements have finite second moments. After obtaining the coefficients b sub k1,..., k sub m, the asymptotic form of these terms for large ... |
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| PATTERN RECOGNITION OF STOCHASTIC PROCESSES. |
07 JUL 1966 |
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| Authors:
Joel Owen; INFORMATION RESEARCH ASSOCIATES INC LEXINGTON MA
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| The class of differential processes are considered. For their class of processes, it is shown that there is an advantage to transforming the observed process x(t) into an infinite vector. Having derived the properties of the vector, it is then shown that the Decision Theory solution to the K-category recognition problems can be formulated in terms of the components of this vector. An example of signal detection is then worked ... |
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| EXTENSIONS TO THEORY OF TIME SERIES ANALYSIS. |
MAY 1966 |
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| Authors:
Walter F. Freiberger; Rolf Adenstedt; BROWN UNIV PROVIDENCE RI DIV OF APPLIED MATHEMATICS
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| We consider a stationary stochastic process (X (sub t): t = 0,1,...) based upon the presence of weather regimes in which the regime indices (K (sub t): t = 0,1,...) form a finite-state stationary ergodic (first-order) Markov chain. The probabilistic problem was considered in previous reports. Here, we now consider the problem of estimating the transition matrix P = (p (sug ij): 1 < or = i,j < or = ... |
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| TESTING AGAINST TREND IN STOCHASTIC PROCESSES. |
08 OCT 1965 |
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| Authors:
H. D. Brunk; D. L. Hanson; MISSOURI UNIV COLUMBIA
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| THE SPECTRAL CHARACTERIZATION AND COMPARISON OF NON-STATIONARY PROCESSES. |
02 AUG 1965 |
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| Authors:
M. R. Dubman; ROCKETDYNE CANOGA PARK CALIF
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| The spectral representation theories of second order stationary, harmonizable, exponentially convex, and normal-type stochastic processes are reviewed and the processes are compared. Locally stationary and asymptotically stationary processes are viewed within the framework of harmonizable and normal-type processes. The concept of a time-dependent spectrum is developed, a general condition for its existence is given, and the time-dependent spectra of harmonizable and normaltype processes are derived. (Author) |
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| ON OPTIMAL STOPPING IN A CLASS OF UNIFORM GAMES. |
JUN 1965 |
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| Authors:
Yuan S. Chow; H. Robbins; COLUMBIA UNIV NEW YORK
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| STOCHASTIC WEAR PROCESSES, |
JUN 1965 |
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| Authors:
Richard Morey; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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| A new class of non-decreasing stochastic processes is characterized. These processes satisfy a generalization of the notion of an increasing failure rate. From physical considerations, these processes seem suitable for describing the process of cumulative wear or damage. The main interest with the model is an investigation of the first time until the process exceeds a random barrier. For this class of processes, it is shown that the first passage ... |
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| STOCHASTIC DUELS WITH HOMING, |
18 MAY 1965 |
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| Authors:
Trevor Williams; SYSTEM DEVELOPMENT CORP SANTA MONICA CALIF
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| Duels where both marksmen 'home' or 'zero in' on one another are here considered, and the effect of this on the win probability is determined. It is proved generally that if the over-all hit probability is fairly and naturally defined, the only possible result of homing must be to worsen a duelist's performance. Next it is shown that a negative binomial distribution of conditional hit probability over rounds exhibits the ... |
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| VARIANCE REDUCTION TECHNIQUES, |
06 MAY 1965 |
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| Authors:
W. L. Maxwell; RAND CORP SANTA MONICA CALIF
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| A variance reduction technique is a procedure which is used in a sampling experiment to reduce the underlying variance of the sample estimates. Such techniques have been used for decades by workers in the social sciences. Kahn, in RM-1237-AEC, presented a catalog of techniques applicable to Monte Carlo sampling experiments. Yet seldom are these techniques employed in the simulation of stochastic processes. The intent is to present some of the ... |
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| THE DISSTRIBUTION OF THE TIME-DURATION OF STOCHASTIC DUELS. |
10 AUG 1964 |
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| Authors:
C. J. Ancker Jr.; A. V. Gafarian; SYSTEM DEVELOPMENT CORP SANTA MONICA CALIF
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| The Theory of Stochastic Duels is extended by considering the distribution of time-to-completion of the fundamental duel. The model has fixed kill probabilities and either random or fixed time between rounds fired. Timelimitation is included. Special cases and examples are worked out. Clearly, the time-duration of combat has both tactical and logistic implications for the decision-maker. (Author) |
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| APPLICATION OF DYNAMIC PROGRAMMING TO STOCHASTIC TIME OPTIMAL CONTROL, |
31 JAN 1964 |
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| Authors:
M. Ash; SYSTEM DEVELOPMENT CORP SANTA MONICA CALIF
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| A non-linear control process is discussed where the control is bounded as absolute value. A random element (noise) that appears additively as part of the control variable is assumed. The performance criterion of driving the system back to equilibrium from its present perturbed state in minimum ''expected'' time, due to the presence of the random noise is used. The principle of optimality of dynamic programming to derive a novel partial ... |
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| A STOCHASTIC MODEL FOR TIME CHANGES IN A BINARY DYADIC RELATION, WITH APPLICATION TO GROUP DYNAMICS. |
11 JUN 1962 |
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| Authors:
T. N. Bhargava; MICHIGAN STATE UNIV EAST LANSING
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| This thesis is concerned with the development of a stochastic model for analyzing time changes in a binary dyadic relation over a finite set of points. For purposes of drawing statistical inference in time the total relation R (A) on the set A is looked upon as an aggregate of its subrelations on subsets of the set A. The number of states in which a subrelation may be found, at ... |
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| BRANCHING PROCESSES, |
29 JUL 1948 |
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| Authors:
T. E. Harris; RAND CORP SANTA MONICA CALIF
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| This paper is concerned with a simple mathematical model for a branching stochastic process. Using the language of family trees we may illustrate the process as follows. The probability that a man has exactly r sons is P sub r, r = 0,1,2,... Each of his sons (who together make up the first generation) has the same probabilities of having a given number of sons of his own; the second ... |
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