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...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2020-05-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2020/50/abstr.html |
| _version_ | 1811338228513374208 |
|---|---|
| author | Julia Calatayud Tomas Caraballo Juan Carlos Cortes Marc Jornet |
| author_facet | Julia Calatayud Tomas Caraballo Juan Carlos Cortes Marc Jornet |
| author_sort | Julia Calatayud |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T18:07:47Z |
| format | Article |
| id | doaj.art-e94fec2cb231436eb810c820714e227f |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-13T18:07:47Z |
| publishDate | 2020-05-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-e94fec2cb231436eb810c820714e227f2022-12-22T02:36:02ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912020-05-01202050,119Mathematical methods for the randomized non-autonomous Bertalanffy modelJulia Calatayud0Tomas Caraballo1Juan Carlos Cortes2Marc Jornet3 Univ. Politecnica de Valencia, Spain Univ. de Sevilla, Spain Univ. Politecnica de Valencia, Spain Univ. Politecnica de Valencia, Spain 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.http://ejde.math.txstate.edu/Volumes/2020/50/abstr.htmlrandom non-autonomous bertalanffy modelrandom differential equationrandom variable transformation techniquekarhunen-loeve expansionprobability density function |
| spellingShingle | Julia Calatayud Tomas Caraballo Juan Carlos Cortes Marc Jornet Mathematical methods for the randomized non-autonomous Bertalanffy model Electronic Journal of Differential Equations random non-autonomous bertalanffy model random differential equation random variable transformation technique karhunen-loeve expansion probability density function |
| title | Mathematical methods for the randomized non-autonomous Bertalanffy model |
| title_full | Mathematical methods for the randomized non-autonomous Bertalanffy model |
| title_fullStr | Mathematical methods for the randomized non-autonomous Bertalanffy model |
| title_full_unstemmed | Mathematical methods for the randomized non-autonomous Bertalanffy model |
| title_short | Mathematical methods for the randomized non-autonomous Bertalanffy model |
| title_sort | mathematical methods for the randomized non autonomous bertalanffy model |
| topic | random non-autonomous bertalanffy model random differential equation random variable transformation technique karhunen-loeve expansion probability density function |
| url | http://ejde.math.txstate.edu/Volumes/2020/50/abstr.html |
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