Refinement of the Main Lemmas of the Theory of Critical Branching Processes
In the paper, we consider critical Markov branching random processes of continuous time and branching random processes of discrete time (critical Galton–Watson processes) defined respectively by the generating functions and In this case, the generating function will be a solution to an ordinary diff...
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| Veröffentlicht in: | Lobachevskii journal of mathematics 2024-07, Vol.45 (7), p.3290-3298 |
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| container_title | Lobachevskii journal of mathematics |
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| creator | Formanov, Sh. K. |
| description | In the paper, we consider critical Markov branching random processes of continuous time and branching random processes of discrete time (critical Galton–Watson processes) defined respectively by the generating functions
and
In this case, the generating function
will be a solution to an ordinary differential equation, the right side of which is a nonlinear function of
and the function
is equal to the number of descendants of one particle at the
-th iteration of the generating function. Asymptotic analysis of generating functions
and
for
respectively, plays a major role in solving the main problems of the theory of branching random processes. Statements related to the asymptotic analysis of generating functions
and
for
respectively, came to be called the main lemmas. |
| doi_str_mv | 10.1134/S1995080224603989 |
| format | Article |
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and
In this case, the generating function
will be a solution to an ordinary differential equation, the right side of which is a nonlinear function of
and the function
is equal to the number of descendants of one particle at the
-th iteration of the generating function. Asymptotic analysis of generating functions
and
for
respectively, plays a major role in solving the main problems of the theory of branching random processes. Statements related to the asymptotic analysis of generating functions
and
for
respectively, came to be called the main lemmas.</description><identifier>ISSN: 1995-0802</identifier><identifier>EISSN: 1818-9962</identifier><identifier>DOI: 10.1134/S1995080224603989</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Algebra ; Analysis ; Asymptotic properties ; Branching (mathematics) ; Differential equations ; Geometry ; Markov processes ; Mathematical Logic and Foundations ; Mathematics ; Mathematics and Statistics ; Probability Theory and Stochastic Processes ; Random processes</subject><ispartof>Lobachevskii journal of mathematics, 2024-07, Vol.45 (7), p.3290-3298</ispartof><rights>Pleiades Publishing, Ltd. 2024</rights><rights>Pleiades Publishing, Ltd. 2024.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c198t-6887644f31917dd49234c9c863bbbeafc07d56c86b19839f93ac963cc8afe1863</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S1995080224603989$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S1995080224603989$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Formanov, Sh. K.</creatorcontrib><title>Refinement of the Main Lemmas of the Theory of Critical Branching Processes</title><title>Lobachevskii journal of mathematics</title><addtitle>Lobachevskii J Math</addtitle><description>In the paper, we consider critical Markov branching random processes of continuous time and branching random processes of discrete time (critical Galton–Watson processes) defined respectively by the generating functions
and
In this case, the generating function
will be a solution to an ordinary differential equation, the right side of which is a nonlinear function of
and the function
is equal to the number of descendants of one particle at the
-th iteration of the generating function. Asymptotic analysis of generating functions
and
for
respectively, plays a major role in solving the main problems of the theory of branching random processes. Statements related to the asymptotic analysis of generating functions
and
for
respectively, came to be called the main lemmas.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Asymptotic properties</subject><subject>Branching (mathematics)</subject><subject>Differential equations</subject><subject>Geometry</subject><subject>Markov processes</subject><subject>Mathematical Logic and Foundations</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Probability Theory and Stochastic Processes</subject><subject>Random processes</subject><issn>1995-0802</issn><issn>1818-9962</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp1kE9PwzAMxSMEEmPwAbhV4lyImy6NjzDxTwyBYJyrNHXWTms6ku6wb0-mgTggTvazf-9ZMmPnwC8BRH71DogTrniW5ZILVHjARqBApYgyO4x9XKe7_TE7CWHJIyilHLGnN7Kto47ckPQ2GRpKnnXrkhl1nQ4_o3lDvd_u1NS3Q2v0Krnx2pmmdYvk1feGQqBwyo6sXgU6-65j9nF3O58-pLOX-8fp9Sw1gGpIpVKFzHMrAKGo6xwzkRs0Soqqqkhbw4t6IqOuIi7QotAGpTBGaUsQsTG72Oeuff-5oTCUy37jXTxZCgCVYYHFJFKwp4zvQ_Bky7VvO-23JfBy97Pyz8-iJ9t7QmTdgvxv8v-mLyoNbJs</recordid><startdate>20240701</startdate><enddate>20240701</enddate><creator>Formanov, Sh. K.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20240701</creationdate><title>Refinement of the Main Lemmas of the Theory of Critical Branching Processes</title><author>Formanov, Sh. K.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c198t-6887644f31917dd49234c9c863bbbeafc07d56c86b19839f93ac963cc8afe1863</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Asymptotic properties</topic><topic>Branching (mathematics)</topic><topic>Differential equations</topic><topic>Geometry</topic><topic>Markov processes</topic><topic>Mathematical Logic and Foundations</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Probability Theory and Stochastic Processes</topic><topic>Random processes</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Formanov, Sh. K.</creatorcontrib><collection>CrossRef</collection><jtitle>Lobachevskii journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Formanov, Sh. K.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Refinement of the Main Lemmas of the Theory of Critical Branching Processes</atitle><jtitle>Lobachevskii journal of mathematics</jtitle><stitle>Lobachevskii J Math</stitle><date>2024-07-01</date><risdate>2024</risdate><volume>45</volume><issue>7</issue><spage>3290</spage><epage>3298</epage><pages>3290-3298</pages><issn>1995-0802</issn><eissn>1818-9962</eissn><abstract>In the paper, we consider critical Markov branching random processes of continuous time and branching random processes of discrete time (critical Galton–Watson processes) defined respectively by the generating functions
and
In this case, the generating function
will be a solution to an ordinary differential equation, the right side of which is a nonlinear function of
and the function
is equal to the number of descendants of one particle at the
-th iteration of the generating function. Asymptotic analysis of generating functions
and
for
respectively, plays a major role in solving the main problems of the theory of branching random processes. Statements related to the asymptotic analysis of generating functions
and
for
respectively, came to be called the main lemmas.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S1995080224603989</doi><tpages>9</tpages></addata></record> |
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| subjects | Algebra Analysis Asymptotic properties Branching (mathematics) Differential equations Geometry Markov processes Mathematical Logic and Foundations Mathematics Mathematics and Statistics Probability Theory and Stochastic Processes Random processes |
| title | Refinement of the Main Lemmas of the Theory of Critical Branching Processes |
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