On strong causal binomial approximation for stochastic processes
This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial processes, i.e., by processes with fixed size binary increments...
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| Format: | Journal Article |
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American Institute of Mathematical Sciences
2014
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| Online Access: | http://hdl.handle.net/20.500.11937/27706 |
| _version_ | 1848752338089541632 |
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| author | Dokuchaev, Nikolai |
| author_facet | Dokuchaev, Nikolai |
| author_sort | Dokuchaev, Nikolai |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial processes, i.e., by processes with fixed size binary increments at sampling points. Moreover, this approximation can be causal, i.e., at every time it requires only past historical values of the underlying process. In addition, possibility of approximation of solutions of stochastic differential equations by solutions of ordinary equations with binary noise is established. Some consequences for the financial modelling and options pricing models are discussed. |
| first_indexed | 2025-11-14T08:07:02Z |
| format | Journal Article |
| id | curtin-20.500.11937-27706 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:07:02Z |
| publishDate | 2014 |
| publisher | American Institute of Mathematical Sciences |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-277062019-02-19T05:35:23Z On strong causal binomial approximation for stochastic processes Dokuchaev, Nikolai incomplete market stochastic processes Donsker Theorem binomial approximation complete market discretisation of Ito equations This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial processes, i.e., by processes with fixed size binary increments at sampling points. Moreover, this approximation can be causal, i.e., at every time it requires only past historical values of the underlying process. In addition, possibility of approximation of solutions of stochastic differential equations by solutions of ordinary equations with binary noise is established. Some consequences for the financial modelling and options pricing models are discussed. 2014 Journal Article http://hdl.handle.net/20.500.11937/27706 10.3934/dcdsb.2014.19.1549 American Institute of Mathematical Sciences fulltext |
| spellingShingle | incomplete market stochastic processes Donsker Theorem binomial approximation complete market discretisation of Ito equations Dokuchaev, Nikolai On strong causal binomial approximation for stochastic processes |
| title | On strong causal binomial approximation for stochastic processes |
| title_full | On strong causal binomial approximation for stochastic processes |
| title_fullStr | On strong causal binomial approximation for stochastic processes |
| title_full_unstemmed | On strong causal binomial approximation for stochastic processes |
| title_short | On strong causal binomial approximation for stochastic processes |
| title_sort | on strong causal binomial approximation for stochastic processes |
| topic | incomplete market stochastic processes Donsker Theorem binomial approximation complete market discretisation of Ito equations |
| url | http://hdl.handle.net/20.500.11937/27706 |