SCIENTIFIC ABSTRACT YAGLOM, A.M. - YAGLOM, I.M.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001961810017-7
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: March 15, 2001
• Sequence Number: 17
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

YA-47 Al.

Yagloax"A. linegir
On
-w-dom pro
mth lacrainedtf, i:,
of n
-Nauk -185-38811954
SSIjRl (N.S.) 94,

he us 4 criWa, and aamifications
Authors Wen 't u
C
I
.
. . .......
r imam oxtmoadq theo
Iryi
continuous Case, romstationay.
as -station'-
stochastic pro~'4 4kh tic
prpcom aving

-6rder~ in&L h
(widi
,
defined and di w4is~e d*
in -a ~previous flik
-Ri
klady'(N.S.). 0.0,, 73t.434:0951).- them' W
~:A:4.
Doab (Urbana
J Frook are omitw.
.
.
j

Polluou and filterm,
doju rucus,,~,-~ with ratt nal --uvc',rFl
deasit, '1.-Ud,,' "tZ.,
hor gv~v, a %~rv ift-4if-I
Oated Ubj,~l tr 1 ,1
Ills: ",ulls w,~Fk: vxt("Ju, I
rigorous and explicit i~-Aatioa!
to pruct~-ses with statmoarv ith ,rAhr w(rements in tte
r revicwcd L?cljw I ht 'A4'1~', U- 11 .1.1
palv
emlier paper (Eec the prtx;~,dn revjewj. L. DoD4
~!p
Flu

e
YAGLOM, Akiva tloiseyevich
YAGLOM, Akiva Moiseyevich Academie'degree of Doctor of Physicomathematical
Sciences, based on his defense, 26 October 1955, in
the Council of the Geophysical Inst Acad Sci USSR,
of his dissertation entitled: "Theory of the correla-
tion of uninterrupted processes and fields with appli-
cation to the problem of statistical eXtrapolation
of temporary series and to the theory of turbulence."
For the Academic Degree of Doctor of Sciences
SO: Byulleten' Ministerstva Vyshego Obrazovaniya SSSR, List No~ 2, 21 January 195L,
Decisions of the Higher Certification Commission concerning academic degrees
and titles.

DOOB, Joseph Leo, 1 10-,; DOBRUSHIR,.R.L.,Ctranslatorl; YAGLOM A.M.,
[tranelator , red. . ....
(Stodhastic Processes) Teraiatnostnye proteessy. Perevod a
an,-,liiskogo.'Kazkva, Izd-vo inostraunoi lit-ry, 1956. 05 p.
(MIRA 11:10)
(Probabilities)

iSRIT cjtl~kysic~ -IGeneral Problems B-1
Ui
ur - rizika,
Abst. Journal :..Ref arat zh No 12, 1936,, 33707
Author Gellfand, I. M., T
aglom, A. M.
n I None
Inatitutto
Titl* Nothods of the Theory of Random Processes in Quantum Physics
Original
Periodical Vestn. Leningr, Uh-ta, 1956, -No 1, 33-34
Abstract i Bri*f Discussion of the possible utilization of methods of the
theory of integration in functional spaces in problems of quantum
mechanics.
Card 1/2

F~WU-VL ERC V'PxIaAce-, Ute-terim; in. tke -s,
lktff those7
hy
R-
Wigner, Pl- 2~ 40 ! I ; 32). 7.

I %I and 'Y agion't A~ t'. Lultegrab"a UD
cOntribut-tcl to by Kac. Canit-ron ?nd Martin, etc., in the
)nf- !~.qnd, and the %v,~-rk r)f Fevn.-njr, a if, othei phys.cvzts
iorimilating quarituin fivid theorv in terms ~-,f integration
macic ai work in qwuttuni theory, rather than in itseff or in
hi '111,r,, i, a f,tlrl-~ !,x!f nsivr-
~vcucn I dek'6ups the theory ut Wie-ier measure Li the
-space of continuous functions, which is related to the heat
;i quation. Attention is given the evaluation of special
integrals along the lines by the work of Kai-.
Amer M:Lth. Sor 6.5 ;3 MR 10, 383,
Lilt- problrm*~
:,uantuin m-Chanics, and e6pecially to the ~)dirddinger
The origin m' th~: ippruach ii apparently thc
(Impublished) Pb.1) iht-iis of Fcyniran, whtj~:t- well-
~mown pqapc-y~ pr ~\ Idl. thr '11:111i PhVS ral basis P)T th~
z"1 4"~A

WIL
SUBJECT USSR/,MATHMTICS/Theory of probability CARD 1/2 PG 995
AUTHOR 41jCLFAND I.M., KOLMOGOROV A.N., TAGLON A.M.
TITLE amoun o=nformation.
On a general definition of an
PERIODICAL Doklady Akad.Nauk 111, 745-748 (1956)
reviewed 7/1957
Let T be a Boolean algebra and let P denote a probability on If Otand
are two finite subalgebras of T , then the expression
P(A B log P(AiBj)
i,j P(Aimp i
is by definition "the amount of information contained in the results of the
experiment 0, relative to the results of the experiment WOL, C
1( Qt)). Generally,
sup Oil? z1)
Ck, Z
where OL and are finite subalgebras; symbolically (1) can be written

Doklady Akad.Nauk 111.,. 745-748 (1956) CARD 2/2 PG 995
,(Oltk) If P(d.Otdt) log. P(dtkdf.)
P(M)P(d Z)
OL
Suppose now that is a Boolean 15'-algebra#P a 6-additive probability
on I*and (X,S X) (SX a IF-algebra) a.measurable space. A random element
of the space X is a homomorphism J*(A) - B of SX into The expression
vp
is taken as definition of the amount of information,
A condition under which I( t,jq) is finite is given. Finally some properties
of this expression are discussed.

%REHM -------
~A
j is"
oft
Ar

A2.
7 PHM I BOUt MIFLOMATION 16
A. MA'Ii6 Yagi
A
. M.5, d cm,, 1. M.
veroyatnost- i infoimatslya (Probaldlity and Mmforustion) No0cow, Gn%,,
195T4 159 Pe 30,000 copies printed.
Ed.: Goryachaya, X. X.; Tech. Ed.; Gavrilov, S. S.; Belilser: Mlolseyeva, Z. V.
-PU WOSB: The book is designed forpeople vithout higher mathezatical education, The
authors' =ain task vas to acquaint the general reader vith certain not-too-
emplicated, but very Uportant mathematical concepts and their application
In modern engineering.
COVERAGE: The fundm2entals of the cUssle theory of prob4ility and the'general
concept of probability in connection vith Boolian A3.gebra -we presented.
7he concepts of entropy wd info2mtion axv Introduced and their
MatIlematIcal formulation given. The Inportavop, 9f t0he CO~Cepts of entropy
and lufmation Is Mustratea by certain log:Lcal problems., Me concepts
of a code and of its econowy are introduced.'
Card 1/.4

Probability and Wormatioa 16
The binary cod e is described and Its econoW studied. The binary --ode is extended
into thIe code of a signals. Sjpealai attention is paid to the Shannon.-ftno Code
and -to Mmonon's work In inrormtion theory. The fundementals of the Shannon-Pano
Co'de and Iis efficiency are' demonstrated. The transmission of a message, when
commmication line disturbances are present is discussed. The Concepts of the
speed of transmission and the carrying capacity of cominlestion lines ale int7,10-
duced and f6rnaas given. No proofs are given for the formijas and only one
Individual case givun by A. No. Kolmogoro4 Is studied. There are 8 references
mentioned in the introduction and In footnotes,.7 of which are Soviet and I Miglish.
In the introduction the authors thank Academician A. No Kolmogorov for his valuable
advice. They also thank editor M. U. Goryachays, for her remarks concerning the
arrangement of the book materials'

d iformation 16
TAiU OF
CONTFMS
Page
Introduction
Ch. I. ProbablUty 7
1. Definition af probability 7
2. Properties of probabIlItys &m and product of events.
InemVistible and. :Lnde]*ndent events 15
Conditlonal'Probabilities 23
4* Algebra of events and the generalized definition of probabUlty 23
eh. n. Patmy and ImformtIon 35
1. Natropy as a,masure of degree of indefiniteness 35
2. Rmtropy of c(upound events, Conditional entropy 43
3- Concept of information 55
.
4* Definition of"eutrapy by its properties 62
Card 3/4

Pr~bability and Thfomation
Ch. In, Solution of Certain Logical Problem vith the Aid of
Calculated Information
1. Simplest Problems
2- Problez of deteruination of a counterfelt coln by veidxing
Ch. IV* Jff~llcatloml of InformtIon fteory to Tmaidsalan of
Messages over Camw2leation Lima
1. Fundamntal concepts. Efficiency of a code
2. Msa=ou-Fano code
3. 'Presence of Usturbances In transidasion of a wasage
Appendix I* Properties of Convex Ametions
Appendix II. Sme 312equalities
AVAMUZZ: Library of Congress
LY-/bmd
Card 4/4 27 Jilne l9sa
5-
16
69
69
78
98
98
108
125
137
152

GRADS~UATNv I.S. (Moscow) R072-AMWO 1PiS.-,(KbAr!k**); HIMOS, R,A. (Moscow)
SIDDPITS~ Z.A. -(-Tkr*s3jii10; GILOYOND- A*0* (kescov); _Wp~o Alma,
(Ifese-ow); RD13INSOIF R.N. (SShX) '=;JD;, '(Yoncov); g~idimy;
SOB. (Moscow)
Problem -of higlier mthemtics. YAtO prom no.l:-224-22? '57-
(MIRA 11:7)
(Mathemdes-Problams, exercises, ate.-)
F,

52-3-2/9
"AUTHOR: Yaglomg Ae Me
TITLE; Gertain Types of Random.-Fields in ti-dimensional Space
Similar to Stationary Stochastic Processes (Nekotoryye
klassy sluchaynykh poley vn,-mernom. prostranstve,
rodstvennyye statsionarnym sluchaynym protsessam.).
PERIODICAL: Teoriya Veroyatnostey i Ye e Primeneniya, 1957, Vol.11,
Nr.:3. pp. 292-337. (USSRT
ABSTRACT: The purpose of this paper is to este.blish a spectral theory
for certain types of random fields and random generalized
fields (multidimensional random distributions) in the
Euclidian n-space Rn similar to the well-known spectral
theory for stationary random processes. Let D denote
the Schwartz space of all complex-valued C..-functions
defined on R whose carrior is compact. Following
T
j
j
It Ref.6) and GeiPand (Ref.7) ive. shall call the random
~
linear functional on
D satisfying
.
2,
"M M of, 4
Card 1/6

Certain Types of Random Fields in a-dimensional Space SimilftT to
Stationary Stochastic Processes.
the random generalized field. We can identify a continuous
random field 1~ (x) on Rn with a random generalized
field
-.CL dL_x_
and therefore w~e, can consider the ordinary random fields
S (1) as special cases of random generalized fields.
We shall only deal with the first moment M(If ) and the
second moment B(y, , cf;,.) of the random generalized field
~, ( y) and shall call them a mean value functional and a
covariance functional of this field. For an ordinary
random field the mean value and covariance function defined
by
! S W = MW (10.) 4 42) = B (.31, 32) (E~- I - I)
play a similar role. The random generalized field
Card 2/6 is called homogeneous if its mean -value functional rr.

52-3-2/9
Certain Types of Random Fields in n-dimensional Space Similar to
Stationary Stochastic Proces-ses.
and covariance functional B( Lfa. are invariant under
'i.e. if the
all shift transformations in the space D,
relations m(y m(-r., and B( tf,
B(T tf ) hold true. The theory of this
Y 2.
homogeneous random generalized ffeld, which is very
similar to 'It'Oh's theory of a stationary random distri-
bution (Ref.6), is treated In section 2. The main'results
of the section concern the spectral representation of the
covariance functional of such fie-Ids and of random general-
ized fields themselves. Let D, denote the subspace of
the space D consisting of all functions (x- satisfying
------ ----
The continuous linear functional 7 on D is called
.Card .3/6 a locally homogeneoue random generalized field if its mean

62-3-2/9
Certain Types of Random Fields, in n-dimensional Space Similar to
Stationary Stochastic ProcessGs.
value, functional W(y and itE~ covariance functional
B( Y, , y2 ) are invariant under all shift transformations
in Di. The locally homogeneous random fields mentioned
above are treated In section 3. In this section we obtain
the spectral representation of a covariance functional of
the. locally homogeneous random generalized field and the
spectral representation of this field itself; these
results generalize the spectral theory for random processes
with stationary increments. The homogeneous random
generalized field is called homogeneous and isotropic if
its mean value functional m(Y ) and covariance functional
B( Lp, , Lp., ) are invariant under all transif ormat ions in D
induced by orthogonal transformations (motions and reflec-,
tions) in the space Rn. - In the case of the n-dimensional
random generalized field op
its mean value functional m(y
lml(~O )"", mn(T
-Card 4/6 forias a vector in R and its covariance functionals
M

.52-3-2/9
'Certain Types of Random Fields in n-dimensional Spece Similar to
Stationary Stochastic Processes.
Bif n. The n-diz_-ensional homogeneous
, ) form a tensor in R
field Y, Of) is called a homogeneous and isotropic random
generalized vector field if the vector and the tonsor are invariant
under all notiolas and refleotiona In RA and the simultaneous
transformations in D induced by this motion or reflection- Homo-
geneous and isotropic random generalized fields and random general-
ized vector fields are treated in section 4. In this section we
obtain the general form of the functionals m(y ) (or m Y))and
B( (or Bij Lp2.)) for these fields. The locally
homogeneous random generalized field '~ ( Y ), Lf C-D, Is called
locally homogeneous and locally isotropic if its mean value
functional ~m( T ) and covariance functional B(tf, , Lf.% ) are
invariant under all transformations in Di induced by orthogonal
transformations in R n ; it is also clear how we can define the
notion of the locally homogeneous and locally iaotropic random
generalized vector field ( Y'), LP E 1), . Locally homogeneous
and locally isotropic ranAom generalized vector fields are treated
Card 6/6

Certain Type's of Random Fields in n-dimensional Space Similar to
Stationary Stochastic Processes.
in secti= 5. Here we obtain the general form of the mean value
functional and of the covariance for these fields; in particular,
we obtain the general form of*-a mean value aa(~ of a covarianee
function of ordinary random fields (scalar ands vector) which are
locally homogeneous and locally isotropic in the sense of
Kolmogorov (Ref.17). There are 31 references, 18 of which are
Slavic.
SUBMITTED: May 7, 1957.
AVAILABLE: Library of Congress.
..Card 6/6

SOV/52-2-4-7/7
A Summary.of Papers Presented at the Sessions of the Scientific
Research Seiiihar on the Theory of Probabilitiej3. N0800w, Feb-XV 1M.
Teorlya,Veroyatzwetey 1 y9ye PrImemnlya, 1957 -Y. 2, No. 4, pp. 478-88
aiLd, x - If this condition is not fulfilled, then
there Is a 'unique solution of Eq.1 taking given values
at. t = 0 and x
a 1 om, A.M.,, C-eneralized locally-homogeneous stochastic
fieigs. 7';Nhe cortents of this paper have been published
in Vol.!2, Xr.3~of this journal. Seregin, L.V., Continuity
conditions with unit probability of strictly Markov
processes. The results are to be published in this
Journal., Yushkevieh, A.A., Strong Markov processes.
The results-were published in Vol.2,,,Nr.2 of this journal.
Tikhomii?ov, V., On S -entropy for Icer.tain alasses of
an alytio functions. The eontents of this report have been
published In Doklady Akad6mii Nauk ' Vol.117, 11r.2, 1957,
p.:191. Urbanik, K., (Wroirlaw), Generalised distributions
at'~*a point of generalised atochastic~ processes. The
generalised stochastic processes are of finite order, i.e.
are generalised derivatives of oontiriuous processes. it
is proved that thedisiribution at a point of a generalised
Card *M process is uniquely defined. Girsanov, I.V., Strongly

SU*BJECT' USSR/VATHEMATICS/Theory of probability CARD 1/4 PO 731
GELFAYD I.M., JAGLOM A.M.
TITLE The conputation of the set of communication about a random
functio-- contained in an other random funot!.on.
PERIODICAL. Vapechi mat.Nauk ILL 19 3-52 (1957)
reviewed 5/1957
The first ohapter in essential correspon4s to the appendix 7 off1hannon and
Weaver "A mathematical theory of communication" but it -3ontains some new
results. Let '~ and q be discrete random terms which can attain the values x
i
(1-1,29 ... n) and yk (k-1,2,...,m) with the probabilities P,(i) and P 1z (k).
~Let Pt7l (ivk) be the probability that at.the same time "~ attains.the value x
and -ithe valuelyk. The set of communication about Yj uontained in-~ then reads
n m
P (i,k) log
i-1 k-1 P (i) Pt(k)
For arbitrary (not discrete) and kL the set of communication is defined as
YL) - sup [~(4, A 0-Y'A ), -q(,6 # I
20 n 11&2#0"' A ml~

UIspech.1. ma:t.Nauk -12 1 3-52 -(1957) CARD 2/4 JPG 131
where the sup has to. be taken over all possible subdivirions of the ranges
of values of and Ytinto finite numbers-of free of oomnon points intervals
A and A ' p respectively.
i k
It is stated that in general the dependence of the set of communication
I( t 9'Yj) on the probability distribution of the pair of vectors is
discontinuous, but that alwikys
Sn- d
n -~o oo
if the sequence ~ng Id converges to with respect to the probability
distribution.
AL further new rest1t is contained in the -theorems In ord.er that I( ~'Vz ) is
finite, it is necessary and sufficient that the probability distribution
P is absolutely continuous with respect to the distribution P~ -Pj Then
01. (XPY) log K(x9y) dpt (x) d.P (y), where
dP'F 4(X,Y)
(X Y) - FLP~ dP,1(7)

espechi mat.Nauk 122. 1, 3-52 (1957) CM 314, PG 731
The second chapter contains an effective computation of I( E,'~L) if the
more-dimensional distributions of the probabilities of 1, YJ and
,are Gaussian. In this case we have
9.9 v 1. log det I- det B
2 det C
vhere L,B,C are the matrices of the second moments of and
If H is the space spanned over all terms. Si, Yt, an& if to the vectors
and rLthere correspondithe subspaces H, and E29 if P, and P2 arethe operators
projecting on H I and H 21 then
7 log det (3 P1P 2pi).
,-For the' concrete computations the authors use a formula which follows from (1)
by putting
A 0 1 A- 0
1 0 B 0 B_
Then

0

Z/507/60/000/000/002/005
W-6 B125/B112
AUTHOR: Yaglom, A. 14. (Moscow)
TITLE: Explicit formulas for the extrapolation, filtration, and
calculation of the informaiion content in the theory of
Gaussian stochastic processes
SOURCE: conference or, Information Theory,-Statistical Decision
Functions, Random Processes.. 2dj' Prague, 1959.
Transactions. Prague, Czal. Academy of Sciences, 1960. 843P.
biblio. 251-262
TEXT: This is a survey of some studies of information theory and the
theory of extrapolation and filtration of. stochastic processes. These
studies have been made during the last few years in Moscow. Special
allowance is made for stationary, Gaussian stochastic processesf(t) with
continuous argument.. Owing to the stationary character also apectral
functions can be used instead of the correlation funciions B(t ) or
1t2
the functionals M1,12).-These spec Itral functions must be determined
from the equations
Card 1/5

Z/507/60/000/000/002/005
Explicit formulas for the B125/B112
B(11, t,)f d.F(Aj
or-
Go
-00
When a stationary process P(t) is extrapolated then the functional of the
Values (t) has to be deterimined-. In the Gaussian catie
T
r
(t I r)=
t(t-s)w(s)ds, (2), where w is a generalized function. The
0
explicit.formulas canbe determined only for.some special cases. In the
most important of these cases the spectral density is rational with
T
respect to :The Fourier transform ~(A) e- w(s)ds of the
.card. 2A

Z/507/60/000/000/002/005
Explicit formulas for the B125/BI12
generalized function w(s) is a rational function analy~;iic in the lower
semi-plane, or an integral function of the form
1(~) and 12()) are rational functions if T
.1 M,e~ 2 0) -
is finite. The filtration problem-of the stationary process ~(t -) consists
in determining the functional A (of the value.sf(tl)) with thelbest
approximation to a fixed random quantity7~.* The filtration problem is
solved similarly to the extrapolation problem if is given by
OW =AQVA) 0-1'-")1 + 0a) + O-ITIO.(A)
This solution in valid almost without change for the generalized
stationary process ~ with rational spectral density. The problems of
,extrapolation, filtration,and interpolation discussed here can be
generalized as follow-s:. for the best approximation by a linear functional
of the valuesof the stationary processfil(t) in a finite number of
intervals not intersecting each other, r the sum of a stationary
Card 3/5

%-g g w4
Z/507/60/000/000/002/005
Explicit formulas for the B125/B112
stochastic process, for a function f(A) with a singularity at .1 - 0 and
for multidimensional extensions of the above problem. The content of
.information is
f Y-1+ k- + (I + jk-) +
Tror) log I
2Y1 + L.
(24)
0 + P)
+
2yi-T-ki
if-f (A=fo=con.,)t and Tt)) isan ordinary stationary process with
ratiUnal. spectral density. k Z-'f2/A.f0If (0) and T-aT. Ae formula for
the specific information is
cc
f log [1 40) da. (26).
Tawl
Card 4/5

i
,]A I,1.~

PHASE I BOOK EUWIMION 807/4175
Yaglom,. Akiva 14oiseyevich., and Isaak Maiseyevich Yaglom
Veroyatnost' i informatsiya (Probability and Information). 2d ed.j, rev. and enl.
Moscovp Fizzatgiz, 1960, 315 p, 25,000 cWies printed.
Ed.: N.G. Sbur; Tech. Ed.: S.N. Akhlanov.
PURPOSE: This book.,the second edition,, is intended for students of higher grades
of secondary schools, university studentsj, teachers in secondary schools and
schools of higher education, commmications engineeras and specialists in
physics., biology,, 3inguisties.. etc.
COVERAGE: The book Is an introduction to a new field of mathematics, information
theory., which is closely connected with cybernetics and has applications in
biology, linguisticeand commmications,. Data on tb~. theoretical and infor-
mational characteristics of specific kinds of messages (written and oral speech,
phototelegrams., television) are cited, The authors thank A.14. Kolmogorov for
his advice on the first edition and acknowledge the assistance given by the

Probability and Information SOY/4175
following on the second edition: S.G. Gindikin, V.I. Levenshteyn, P.S. Norvikov,
I.A. Ovseyevich, S.M', Rytov,, V.A. UspenBkiy., G.A. Shestopal, M.I. Eydellnant,
R.L. Dobrusbin., A.A. Kharkevich., V.A, G sh.# L.R.'Zinderp D.S. lebedevand
T.N. Moloshna. There are 54 references: 29 Soviet (including translations),,
21 English and 4 German.
TAM OF COMM
From the Foreword to the First Edition
Foreword to the Second Edition
Ch. I., Probability 13
1. Definition of probability 13
2. Properties of probability. ~Addition and awltiplication of
-~events. Inc*ampatible and independent ev ents 21
3. Conditional probabilities 29
4. Algebra,of.events and. a general definition of probability 36
Ch. Il. Entro;ry and Information 44
1. Entropy as a measure of the degree of indeterminacy 44
2. Entropy of compound events. CondItional entropy 62
Card 2*"~L

83217
S/052/60/005/003/001/GO2
C III/C222
'AUTHORs Yaglom, A. 1K.
........ .
t
TITLEi-Ef otive-Solutiona of Linear Approxims, io Problems for
Multiveriate Stationary ProcessealWith a Rational Spectrum
PERIODICAL: Te'toriya veroyatnostey i yeyepprimeneniye. 1960, Vol.5,
No.3, pp.265-292. V,
TEXTs The author considers multivariate stationary processes
_oD O>k:
(r) and bg&) in- the inertial ifit e~veil
:_6i~ elre~'.L -and 1,v Are - thUe external and -internall scales of the turbulence)
cnd~.tbe: corresr'i'onding Iffive-thirds" law f or the velocity
in: the ''interval... k,