O’zbekiston respublikasi oliy va o’rta maxsus ta’lim vazirligi mirzo ulug’bek nomidagi o’zbekiston milliy universiteti fakulteti

Ilmiy rahbar: Dots.AzimovJ.B. Magistratura talabasi: Vohobjonov J.X
MINISTRY OF HIGHER AND SECONDARY SPECIAL EDUCATION OF THE REPUBLIC OF UZBEKISTAN
NATIONAL UNIVERSITY OF UZBEKISTAN NAMED AFTER MIRZO ULUGBEK
Faculty: Mathematics Master’s student: Vokhobjonov J.X
Department: Probability theory Supervisor: J.B.Azimov
of and mathematical statistics Speciality: 5A130102- Probability
Academic year: 2021-2023 theory of and mathematical statistics
of master’s dissertation on the subjects of:
ANNOTATION
“Asymptotic analysis of Foster-Pakes’ branching processes with decreasing immigration”
Priority of the topic: In the theory of the random processes branching processes play an important role. Because, branching random processes can be used as a mathematical model of natural processes in many fields such as demography, medicine, nuclear physics. In this master’s dissertation asymptotic properties of Foster-Peykes’ branching processes are learned. Initially these processes were entered by Foster, when the number of particles is exhausted, it comes and joins to the process of immigration components in the random quantity, and this process is continued. Learning and researching asymptotic properties of this processes is important.
Object and subject of research : Foster-Peykes’ random processes with decreasing immigration and their asymptotic properties.
Scientific novelty of the research : Branching processes with immigration depending on several states were studied. For example, a limit theorem for the probability of non-extinction of Foster-Pakes random processes with decreasing immigration is proved.
Scientific supervisor : J.B.Azimov
Master's student: J.X Vokhobjonov

MUNDARIJA

KIRISH 4
1.1 Xarakteristik funksiya va uning xossalari 7
1.2. Hosil qilish funksiyalar va ularning xossalari. 17
1.3. Hosil qiluvchi funksiyalarning qo’llanilishi 22
I –bob bo’yicha xulosa. 27
II-bob. TARMOQLANUVCHI TASODIFIY JARAYONLAR 29
2.1 Galton-Vatson tarmoqlanuvchi tasodifiy jarayonlari 29
2.2. Immigratsiyali Galton-Vatson tarmoqlanuvchi tasodifiy jarayonlari 36
2.3. Foster-Peykes tarmoqlanuvchi tasodifiy jarayonlari va ularning asimptotik tahlili 40
II –bob bo’yicha xulosa 42