Applied methods of the theory of random functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Oxford [u.a.]
Pergamon Press
1966
|
| Series: | International series of monographs on pure and applied mathematics
89 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 321 S. Ill., graph. Darst. |
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| 240 | 1 | 0 | |a Prikladnye metody teorii slučajnych funkcij |
| 245 | 1 | 0 | |a Applied methods of the theory of random functions |c A. A. Sveshnikov |
| 264 | 1 | |a Oxford [u.a.] |b Pergamon Press |c 1966 | |
| 300 | |a IX, 321 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
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| adam_text | CONTENTS
Pub usher s Note ix
Chapter I. General Properties of Random Functions 1
§ 1. The theory of random functions as a branch of the
theory of probability 1
§ 2. The basic notations and formulae of the theory of
probability 3
§ 3. Eandom functions and methods of describing them 11
§ 4. Typical problems, solved by means of the theory of
random functions 21
§ 5. Properties of the correlation function 25
§ 6. The differentiation and integration of random func¬
tions 31
§ 7. The action of a linear operator on a random function 46
§ 8. A system of random functions. The cross correla¬
tion function 62
§ 9. Problems on overshoots: the mean number of over¬
shoots of a random function above a given level, the
mean duration of an overshoot 69
Chapter II. The Spectral Theory of Stationary
Random Functions 81
§ 10. The spectral representation of stationary random
functions 81
§ 11. Examples of the calculation of the spectral density
of a stationary random process 95
§ 12. The spectral density of a linear combination of a
stationary random function and its derivatives. The
stationary solution of a linear differential equation
¦with constant coefficients 102
T
Vi CONTENTS
§ 13. Examples of spectral densities and correlation func¬
tions in more complicated cases 114
§ 14. Determination of the correlation function of the
solution of a non homogeneous differential equation
with constant coefficients when the right hand side
is non stationary 127
§ 15. Linear differential equations with variable coeffi¬
cients 134
§ 16. The probability characteristics of the solutions of
a system of linear equations 139
§ 17. The density distribution of the solution of a linear
differential equation 157
Chapter m. Determination of Optimal Dynamical
Systems 163
§ 18. Statement of the problem of the determination of
optimal systems 163
§ 19. The general solution of the problem of determining (gi¬
ven the infinite past of the process) the optimal dyna¬
mical system representing the operations of smoothing
(filtering), extrapolation and differentiation 176
§ 20. Formulae for the determination of the optimal trans¬
fer function of a dynamical system performing filtra¬
tion, extrapolation and differentiation in the case of
rational spectral densities of signal and noise 190
§ 21. Practical formulae for the optimal transfer function
of a dynamical system with delay 195
§ 22. Optimal smoothing, extrapolation and differentiation
for a finite observation time 201
§ 23. Examples of the determination of optimal dynamical
systems for a finite observation time 216
Chatter IV. Experimental Methods fob the Deter¬
mination of Characteristics of Random Functions 225
§ 24. The general principles of the determination of
characteristics of random functions from experimental
data 225
CONTENTS vii
§ 25. The principles of the construction of correlators —
devices for the determination of the correlation
functions of stationary random processes 242
§ 26. Determination of the estimated value of the spectral
density 249
Chapter V. The Method ov Envelopes 256
§ 27. The method of envelopes and the derivation of gen¬
eral formulae 256
§ 28. Application of the method of envelopes in the case
of a narrow band spectrum 274
Chapteb VI. Some Stopplementaby Problems of the
Theoby or Random Fitnotions 287
§ 29. Random sequences 287
§ 30. Random functions of many variables 296
§ 31. Canonical expansions of random functions 305
References 311
Index 313
Other Titles nsr this Sebies 319
|
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| author | Svešnikov, Aram A. 1911-1979 |
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| indexdate | 2024-07-09T16:58:36Z |
| institution | BVB |
| language | English Russian |
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| physical | IX, 321 S. Ill., graph. Darst. |
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| publishDate | 1966 |
| publishDateSearch | 1966 |
| publishDateSort | 1966 |
| publisher | Pergamon Press |
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| series | International series of monographs on pure and applied mathematics |
| series2 | International series of monographs on pure and applied mathematics |
| spelling | Svešnikov, Aram A. 1911-1979 Verfasser (DE-588)172391792 aut Prikladnye metody teorii slučajnych funkcij Applied methods of the theory of random functions A. A. Sveshnikov Oxford [u.a.] Pergamon Press 1966 IX, 321 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series of monographs on pure and applied mathematics 89 Zufallsfunktion (DE-588)4191096-5 gnd rswk-swf Zufallsfunktion (DE-588)4191096-5 s 1\p DE-604 International series of monographs on pure and applied mathematics 89 (DE-604)BV001888024 89 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004655509&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Svešnikov, Aram A. 1911-1979 Applied methods of the theory of random functions International series of monographs on pure and applied mathematics Zufallsfunktion (DE-588)4191096-5 gnd |
| subject_GND | (DE-588)4191096-5 |
| title | Applied methods of the theory of random functions |
| title_alt | Prikladnye metody teorii slučajnych funkcij |
| title_auth | Applied methods of the theory of random functions |
| title_exact_search | Applied methods of the theory of random functions |
| title_full | Applied methods of the theory of random functions A. A. Sveshnikov |
| title_fullStr | Applied methods of the theory of random functions A. A. Sveshnikov |
| title_full_unstemmed | Applied methods of the theory of random functions A. A. Sveshnikov |
| title_short | Applied methods of the theory of random functions |
| title_sort | applied methods of the theory of random functions |
| topic | Zufallsfunktion (DE-588)4191096-5 gnd |
| topic_facet | Zufallsfunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004655509&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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