Asymptotic behavior of functionals of the solutions to inhomogeneous Itô stochastic differential equations with nonregular dependence on parameter
The asymptotic behavior, as $T\to \infty $, of some functionals of the form $I_{T}(t)=F_{T}(\xi _{T}(t))+{\int _{0}^{t}}g_{T}(\xi _{T}(s))\hspace{0.1667em}dW_{T}(s)$, $t\ge 0$ is studied. Here $\xi _{T}(t)$ is the solution to the time-inhomogeneous Itô stochastic differential equation \[d\xi _{T}(t)...
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| Format: | Article |
| Language: | English |
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VTeX
2017-09-01
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| Series: | Modern Stochastics: Theory and Applications |
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| Online Access: | https://vmsta.vtex.vmt/doi/10.15559/17-VMSTA83 |
| _version_ | 1818821595154612224 |
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| author | Grigorij Kulinich Svitlana Kushnirenko |
| author_facet | Grigorij Kulinich Svitlana Kushnirenko |
| author_sort | Grigorij Kulinich |
| collection | DOAJ |
| description | The asymptotic behavior, as $T\to \infty $, of some functionals of the form $I_{T}(t)=F_{T}(\xi _{T}(t))+{\int _{0}^{t}}g_{T}(\xi _{T}(s))\hspace{0.1667em}dW_{T}(s)$, $t\ge 0$ is studied. Here $\xi _{T}(t)$ is the solution to the time-inhomogeneous Itô stochastic differential equation \[d\xi _{T}(t)=a_{T}\big(t,\xi _{T}(t)\big)\hspace{0.1667em}dt+dW_{T}(t),\hspace{1em}t\ge 0,\hspace{2.5pt}\xi _{T}(0)=x_{0},\] $T>0$ is a parameter, $a_{T}(t,x),x\in \mathbb{R}$ are measurable functions, $|a_{T}(t,x)|\le C_{T}$ for all $x\in \mathbb{R}$ and $t\ge 0$, $W_{T}(t)$ are standard Wiener processes, $F_{T}(x),x\in \mathbb{R}$ are continuous functions, $g_{T}(x),x\in \mathbb{R}$ are measurable locally bounded functions, and everything is real-valued. The explicit form of the limiting processes for $I_{T}(t)$ is established under nonregular dependence of $a_{T}(t,x)$ and $g_{T}(x)$ on the parameter T. |
| first_indexed | 2024-12-18T23:10:41Z |
| format | Article |
| id | doaj.art-c5faa7197a83406eb2b11ccde5658583 |
| institution | Directory Open Access Journal |
| issn | 2351-6046 2351-6054 |
| language | English |
| last_indexed | 2024-12-18T23:10:41Z |
| publishDate | 2017-09-01 |
| publisher | VTeX |
| record_format | Article |
| series | Modern Stochastics: Theory and Applications |
| spelling | doaj.art-c5faa7197a83406eb2b11ccde56585832022-12-21T20:48:21ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542017-09-014319921710.15559/17-VMSTA83Asymptotic behavior of functionals of the solutions to inhomogeneous Itô stochastic differential equations with nonregular dependence on parameterGrigorij Kulinich0Svitlana Kushnirenko1Taras Shevchenko National University of Kyiv, 64/13, Volodymyrska Street, 01601 Kyiv, UkraineTaras Shevchenko National University of Kyiv, 64/13, Volodymyrska Street, 01601 Kyiv, UkraineThe asymptotic behavior, as $T\to \infty $, of some functionals of the form $I_{T}(t)=F_{T}(\xi _{T}(t))+{\int _{0}^{t}}g_{T}(\xi _{T}(s))\hspace{0.1667em}dW_{T}(s)$, $t\ge 0$ is studied. Here $\xi _{T}(t)$ is the solution to the time-inhomogeneous Itô stochastic differential equation \[d\xi _{T}(t)=a_{T}\big(t,\xi _{T}(t)\big)\hspace{0.1667em}dt+dW_{T}(t),\hspace{1em}t\ge 0,\hspace{2.5pt}\xi _{T}(0)=x_{0},\] $T>0$ is a parameter, $a_{T}(t,x),x\in \mathbb{R}$ are measurable functions, $|a_{T}(t,x)|\le C_{T}$ for all $x\in \mathbb{R}$ and $t\ge 0$, $W_{T}(t)$ are standard Wiener processes, $F_{T}(x),x\in \mathbb{R}$ are continuous functions, $g_{T}(x),x\in \mathbb{R}$ are measurable locally bounded functions, and everything is real-valued. The explicit form of the limiting processes for $I_{T}(t)$ is established under nonregular dependence of $a_{T}(t,x)$ and $g_{T}(x)$ on the parameter T.https://vmsta.vtex.vmt/doi/10.15559/17-VMSTA83Diffusion-type processesasymptotic behavior of functionalsnonregular dependence on the parameter |
| spellingShingle | Grigorij Kulinich Svitlana Kushnirenko Asymptotic behavior of functionals of the solutions to inhomogeneous Itô stochastic differential equations with nonregular dependence on parameter Modern Stochastics: Theory and Applications Diffusion-type processes asymptotic behavior of functionals nonregular dependence on the parameter |
| title | Asymptotic behavior of functionals of the solutions to inhomogeneous Itô stochastic differential equations with nonregular dependence on parameter |
| title_full | Asymptotic behavior of functionals of the solutions to inhomogeneous Itô stochastic differential equations with nonregular dependence on parameter |
| title_fullStr | Asymptotic behavior of functionals of the solutions to inhomogeneous Itô stochastic differential equations with nonregular dependence on parameter |
| title_full_unstemmed | Asymptotic behavior of functionals of the solutions to inhomogeneous Itô stochastic differential equations with nonregular dependence on parameter |
| title_short | Asymptotic behavior of functionals of the solutions to inhomogeneous Itô stochastic differential equations with nonregular dependence on parameter |
| title_sort | asymptotic behavior of functionals of the solutions to inhomogeneous ito stochastic differential equations with nonregular dependence on parameter |
| topic | Diffusion-type processes asymptotic behavior of functionals nonregular dependence on the parameter |
| url | https://vmsta.vtex.vmt/doi/10.15559/17-VMSTA83 |
| work_keys_str_mv | AT grigorijkulinich asymptoticbehavioroffunctionalsofthesolutionstoinhomogeneousitostochasticdifferentialequationswithnonregulardependenceonparameter AT svitlanakushnirenko asymptoticbehavioroffunctionalsofthesolutionstoinhomogeneousitostochasticdifferentialequationswithnonregulardependenceonparameter |