Mathematical methods for the randomized non-autonomous Bertalanffy model
In this article we analyze the randomized non-autonomous Bertalanffy model $$ x'(t,\omega)=a(t,\omega)x(t,\omega)+b(t,\omega)x(t,\omega)^{2/3},\quad x(t_0,\omega)=x_0(\omega), $$ where $a(t,\omega)$ and $b(t,\omega)$ are stochastic processes and $x_0(\omega)$ is a random variable, all of them d...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Julia Calatayud [verfasserIn] Tomas Caraballo [verfasserIn] Juan Carlos Cortes [verfasserIn] Marc Jornet [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
random non-autonomous bertalanffy model |
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| Übergeordnetes Werk: |
In: Electronic Journal of Differential Equations - Texas State University, 2003, (2020), 50,, Seite 19 |
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| Übergeordnetes Werk: |
year:2020 ; number:50, ; pages:19 |
| Links: |
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DOAJ028028120 |
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| 520 | |a In this article we analyze the randomized non-autonomous Bertalanffy model $$ x'(t,\omega)=a(t,\omega)x(t,\omega)+b(t,\omega)x(t,\omega)^{2/3},\quad x(t_0,\omega)=x_0(\omega), $$ where $a(t,\omega)$ and $b(t,\omega)$ are stochastic processes and $x_0(\omega)$ is a random variable, all of them defined in an underlying complete probability space. Under certain assumptions on a, b and $x_0$, we obtain a solution stochastic process, $x(t,\omega)$, both in the sample path and in the mean square senses. By using the random variable transformation technique and Karhunen-Loeve expansions, we construct a sequence of probability density functions that under certain conditions converge pointwise or uniformly to the density function of $x(t,\omega)$, $f_{x(t)}(x)$. This permits approximating the expectation and the variance of $x(t,\omega)$. At the end, numerical experiments are carried out to put in practice our theoretical findings. | ||
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(DE-627)DOAJ028028120 (DE-599)DOAJe94fec2cb231436eb810c820714e227f DE-627 ger DE-627 rakwb eng QA1-939 Julia Calatayud verfasserin aut Mathematical methods for the randomized non-autonomous Bertalanffy model 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this article we analyze the randomized non-autonomous Bertalanffy model $$ x'(t,\omega)=a(t,\omega)x(t,\omega)+b(t,\omega)x(t,\omega)^{2/3},\quad x(t_0,\omega)=x_0(\omega), $$ where $a(t,\omega)$ and $b(t,\omega)$ are stochastic processes and $x_0(\omega)$ is a random variable, all of them defined in an underlying complete probability space. Under certain assumptions on a, b and $x_0$, we obtain a solution stochastic process, $x(t,\omega)$, both in the sample path and in the mean square senses. By using the random variable transformation technique and Karhunen-Loeve expansions, we construct a sequence of probability density functions that under certain conditions converge pointwise or uniformly to the density function of $x(t,\omega)$, $f_{x(t)}(x)$. This permits approximating the expectation and the variance of $x(t,\omega)$. At the end, numerical experiments are carried out to put in practice our theoretical findings. random non-autonomous bertalanffy model random differential equation random variable transformation technique karhunen-loeve expansion probability density function Mathematics Tomas Caraballo verfasserin aut Juan Carlos Cortes verfasserin aut Marc Jornet verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2020), 50,, Seite 19 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2020 number:50, pages:19 https://doaj.org/article/e94fec2cb231436eb810c820714e227f kostenfrei http://ejde.math.txstate.edu/Volumes/2020/50/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2020 50, 19 |
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(DE-627)DOAJ028028120 (DE-599)DOAJe94fec2cb231436eb810c820714e227f DE-627 ger DE-627 rakwb eng QA1-939 Julia Calatayud verfasserin aut Mathematical methods for the randomized non-autonomous Bertalanffy model 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this article we analyze the randomized non-autonomous Bertalanffy model $$ x'(t,\omega)=a(t,\omega)x(t,\omega)+b(t,\omega)x(t,\omega)^{2/3},\quad x(t_0,\omega)=x_0(\omega), $$ where $a(t,\omega)$ and $b(t,\omega)$ are stochastic processes and $x_0(\omega)$ is a random variable, all of them defined in an underlying complete probability space. Under certain assumptions on a, b and $x_0$, we obtain a solution stochastic process, $x(t,\omega)$, both in the sample path and in the mean square senses. By using the random variable transformation technique and Karhunen-Loeve expansions, we construct a sequence of probability density functions that under certain conditions converge pointwise or uniformly to the density function of $x(t,\omega)$, $f_{x(t)}(x)$. This permits approximating the expectation and the variance of $x(t,\omega)$. At the end, numerical experiments are carried out to put in practice our theoretical findings. random non-autonomous bertalanffy model random differential equation random variable transformation technique karhunen-loeve expansion probability density function Mathematics Tomas Caraballo verfasserin aut Juan Carlos Cortes verfasserin aut Marc Jornet verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2020), 50,, Seite 19 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2020 number:50, pages:19 https://doaj.org/article/e94fec2cb231436eb810c820714e227f kostenfrei http://ejde.math.txstate.edu/Volumes/2020/50/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2020 50, 19 |
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(DE-627)DOAJ028028120 (DE-599)DOAJe94fec2cb231436eb810c820714e227f DE-627 ger DE-627 rakwb eng QA1-939 Julia Calatayud verfasserin aut Mathematical methods for the randomized non-autonomous Bertalanffy model 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this article we analyze the randomized non-autonomous Bertalanffy model $$ x'(t,\omega)=a(t,\omega)x(t,\omega)+b(t,\omega)x(t,\omega)^{2/3},\quad x(t_0,\omega)=x_0(\omega), $$ where $a(t,\omega)$ and $b(t,\omega)$ are stochastic processes and $x_0(\omega)$ is a random variable, all of them defined in an underlying complete probability space. Under certain assumptions on a, b and $x_0$, we obtain a solution stochastic process, $x(t,\omega)$, both in the sample path and in the mean square senses. By using the random variable transformation technique and Karhunen-Loeve expansions, we construct a sequence of probability density functions that under certain conditions converge pointwise or uniformly to the density function of $x(t,\omega)$, $f_{x(t)}(x)$. This permits approximating the expectation and the variance of $x(t,\omega)$. At the end, numerical experiments are carried out to put in practice our theoretical findings. random non-autonomous bertalanffy model random differential equation random variable transformation technique karhunen-loeve expansion probability density function Mathematics Tomas Caraballo verfasserin aut Juan Carlos Cortes verfasserin aut Marc Jornet verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2020), 50,, Seite 19 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2020 number:50, pages:19 https://doaj.org/article/e94fec2cb231436eb810c820714e227f kostenfrei http://ejde.math.txstate.edu/Volumes/2020/50/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2020 50, 19 |
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(DE-627)DOAJ028028120 (DE-599)DOAJe94fec2cb231436eb810c820714e227f DE-627 ger DE-627 rakwb eng QA1-939 Julia Calatayud verfasserin aut Mathematical methods for the randomized non-autonomous Bertalanffy model 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this article we analyze the randomized non-autonomous Bertalanffy model $$ x'(t,\omega)=a(t,\omega)x(t,\omega)+b(t,\omega)x(t,\omega)^{2/3},\quad x(t_0,\omega)=x_0(\omega), $$ where $a(t,\omega)$ and $b(t,\omega)$ are stochastic processes and $x_0(\omega)$ is a random variable, all of them defined in an underlying complete probability space. Under certain assumptions on a, b and $x_0$, we obtain a solution stochastic process, $x(t,\omega)$, both in the sample path and in the mean square senses. By using the random variable transformation technique and Karhunen-Loeve expansions, we construct a sequence of probability density functions that under certain conditions converge pointwise or uniformly to the density function of $x(t,\omega)$, $f_{x(t)}(x)$. This permits approximating the expectation and the variance of $x(t,\omega)$. At the end, numerical experiments are carried out to put in practice our theoretical findings. random non-autonomous bertalanffy model random differential equation random variable transformation technique karhunen-loeve expansion probability density function Mathematics Tomas Caraballo verfasserin aut Juan Carlos Cortes verfasserin aut Marc Jornet verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2020), 50,, Seite 19 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2020 number:50, pages:19 https://doaj.org/article/e94fec2cb231436eb810c820714e227f kostenfrei http://ejde.math.txstate.edu/Volumes/2020/50/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2020 50, 19 |
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(DE-627)DOAJ028028120 (DE-599)DOAJe94fec2cb231436eb810c820714e227f DE-627 ger DE-627 rakwb eng QA1-939 Julia Calatayud verfasserin aut Mathematical methods for the randomized non-autonomous Bertalanffy model 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this article we analyze the randomized non-autonomous Bertalanffy model $$ x'(t,\omega)=a(t,\omega)x(t,\omega)+b(t,\omega)x(t,\omega)^{2/3},\quad x(t_0,\omega)=x_0(\omega), $$ where $a(t,\omega)$ and $b(t,\omega)$ are stochastic processes and $x_0(\omega)$ is a random variable, all of them defined in an underlying complete probability space. Under certain assumptions on a, b and $x_0$, we obtain a solution stochastic process, $x(t,\omega)$, both in the sample path and in the mean square senses. By using the random variable transformation technique and Karhunen-Loeve expansions, we construct a sequence of probability density functions that under certain conditions converge pointwise or uniformly to the density function of $x(t,\omega)$, $f_{x(t)}(x)$. This permits approximating the expectation and the variance of $x(t,\omega)$. At the end, numerical experiments are carried out to put in practice our theoretical findings. random non-autonomous bertalanffy model random differential equation random variable transformation technique karhunen-loeve expansion probability density function Mathematics Tomas Caraballo verfasserin aut Juan Carlos Cortes verfasserin aut Marc Jornet verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2020), 50,, Seite 19 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2020 number:50, pages:19 https://doaj.org/article/e94fec2cb231436eb810c820714e227f kostenfrei http://ejde.math.txstate.edu/Volumes/2020/50/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2020 50, 19 |
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Mathematical methods for the randomized non-autonomous Bertalanffy model |
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In this article we analyze the randomized non-autonomous Bertalanffy model $$ x'(t,\omega)=a(t,\omega)x(t,\omega)+b(t,\omega)x(t,\omega)^{2/3},\quad x(t_0,\omega)=x_0(\omega), $$ where $a(t,\omega)$ and $b(t,\omega)$ are stochastic processes and $x_0(\omega)$ is a random variable, all of them defined in an underlying complete probability space. Under certain assumptions on a, b and $x_0$, we obtain a solution stochastic process, $x(t,\omega)$, both in the sample path and in the mean square senses. By using the random variable transformation technique and Karhunen-Loeve expansions, we construct a sequence of probability density functions that under certain conditions converge pointwise or uniformly to the density function of $x(t,\omega)$, $f_{x(t)}(x)$. This permits approximating the expectation and the variance of $x(t,\omega)$. At the end, numerical experiments are carried out to put in practice our theoretical findings. |
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In this article we analyze the randomized non-autonomous Bertalanffy model $$ x'(t,\omega)=a(t,\omega)x(t,\omega)+b(t,\omega)x(t,\omega)^{2/3},\quad x(t_0,\omega)=x_0(\omega), $$ where $a(t,\omega)$ and $b(t,\omega)$ are stochastic processes and $x_0(\omega)$ is a random variable, all of them defined in an underlying complete probability space. Under certain assumptions on a, b and $x_0$, we obtain a solution stochastic process, $x(t,\omega)$, both in the sample path and in the mean square senses. By using the random variable transformation technique and Karhunen-Loeve expansions, we construct a sequence of probability density functions that under certain conditions converge pointwise or uniformly to the density function of $x(t,\omega)$, $f_{x(t)}(x)$. This permits approximating the expectation and the variance of $x(t,\omega)$. At the end, numerical experiments are carried out to put in practice our theoretical findings. |
| abstract_unstemmed |
In this article we analyze the randomized non-autonomous Bertalanffy model $$ x'(t,\omega)=a(t,\omega)x(t,\omega)+b(t,\omega)x(t,\omega)^{2/3},\quad x(t_0,\omega)=x_0(\omega), $$ where $a(t,\omega)$ and $b(t,\omega)$ are stochastic processes and $x_0(\omega)$ is a random variable, all of them defined in an underlying complete probability space. Under certain assumptions on a, b and $x_0$, we obtain a solution stochastic process, $x(t,\omega)$, both in the sample path and in the mean square senses. By using the random variable transformation technique and Karhunen-Loeve expansions, we construct a sequence of probability density functions that under certain conditions converge pointwise or uniformly to the density function of $x(t,\omega)$, $f_{x(t)}(x)$. This permits approximating the expectation and the variance of $x(t,\omega)$. At the end, numerical experiments are carried out to put in practice our theoretical findings. |
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Mathematical methods for the randomized non-autonomous Bertalanffy model |
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https://doaj.org/article/e94fec2cb231436eb810c820714e227f http://ejde.math.txstate.edu/Volumes/2020/50/abstr.html https://doaj.org/toc/1072-6691 |
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Tomas Caraballo Juan Carlos Cortes Marc Jornet |
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