CIA-RDP82-00039R000100230003-3.pdf

Declassified in Part - Sanitized Copy Approved for Release 2012/05/10 : CIA-RDP82-00039R000100230003-3 STAT Introduction to the Theory of Branching Stochastic Precesses B. A. Sevasttyanov; Uspekhi Matematicheskikh Nauk, Volume VI, No 6 (46), pages 17-99. Moscow/Leningrad: Nov-Dec 1951. STAT Declassified in Part - Sanitized Copy Approved for Release 2012/05/10 : CIA-RDP82-00039R000100230003-3

© Declassified in Part - Sanitized Copy Approv Release 2012/05/10 : CIA-RDP82-00039R000100230003-3 noe - “ ‘, STAT . a Introdaeticn to the Thoory of Branching Stechestie Procesese ' Be Bo Sevast*yanovs Uepekh’ Matematicheskikh STAT es Declassified in Part - Sanitized Copy Approved for Release 2012/05/10 : CIA-RDP82-00039R000100230003-3

Declassified in Part - Sanitized Copy Approved 1 for F Release 2012/05/10. CIA-! RDP82- 00039R000100230003- 3 % Bo Ae Sevast'yanov ¥ [Note The following article representa the firet t section, entitled ‘ ‘Introduction, to the report, “Theory of Branching Stoshas*.ic Processes", which. ‘appeared in the journal Uspekhi Matematicheskikh Nauk, Volume om oon NowfDee 14g fuss , *scuchaynyye proteessy" (omyyaiinme rTpoueccnt) J se YiIy No'$ (6) ggpages 7-99. The: expression Patochastic processes" is in ay Ni a In pnyeica and chemistry oosur nny Phenomena which are coments with, : “ no eda mage ee te …

Declassified in Part - Sanitized Copy Approved for Release 2012/05/10 : CIA-RDP82-00039R000100230003-3 AGG ciate wees wt ARETE ge we mees bepioning of the reestien to sansiéer thet hata will oot break. fies, ane Cl atom starte te follaring chain of reestions CleH, ey eHC] (a) “4 H *Cl,* CleHcl 4 paring oaloletions ef the initial stage af the resstion we cen consider the ele concentrations of H, and Cl, as invariable. Taken inte consideration in ealev- ‘ Lat tone are only those particles which are scarce at tne beginming of ths reaction. in our example this will be Cl and H stens and HCL molecu…

* a eae CIA-RDP82-00039R000100230 es ee Ss needle rem sn interval of tine bt with probability pat ¢ o(tt) inte Ty * Tye “et vl fi tine At and with the same probébility particle of type t, be transformed ering oa va td PX t) nat ot voment of tine t there are 6, particles of t7Pe Ty: Tne provebility satisfies the systes of differential equations ae a v te \ - vere gS for p 4 a ie the probability dansity of the seneitn see Yq z @ to the state &, and ed is the probability density of m encey wy the * prom the state @- It in easily seen that in our case o4 is deterained La following we ort Op if Pro…

Declassified in Part - itized Copy Approved for Release 2012/05/10 : CIA-RDP82-00039R000100230003-3 4 re ty 4 5, . F(t; soak) Re Expanding (10) in powers of X,0%)2%, ve find the desired probabilities: | PO0r2e) wo (pe) /aPO (aes, wlOetetrD), (948d pt (zeea)t 4 Since wo have M, (t) bd @(t42,2,1)/ae, r) then differentiating (8) with respect te %, and ootting x,°x,"x,"1 we obtein the first equation for the methemstical expectations of aystea (3). The remaining two equations of eystem (3) are obtained if we differentiete (8) with respect te X, and x, respectively. We note here that the seefficieat…

Me Declassified in Part - Saniti : : -Sa . . ~ of initized Copy Approved for Release 2012/05/10 : CIA-RDP82-00039R - 82 000100230003-3 In particulars H,( 00) = p/e solving eqeation (11) we find the gener F(tsx vets)! F(t, Kye 2 tt 1s easy to 868 that as tea the "particles of typeset TY and. "9 sooner oT FZ mM eines (eprité 5 Pd = ort (ort erty a) . Later will He out and only particles of the type tT; will rama, the — of | wract, wil never diminish after this. From (13) it is 0a8y to deduct that the prorat iistins Wo that the finel number of particles af type T. wild bavel » viven , i qunber & …