Markov chain approximations to stochastic differential equations by recombination on lattice trees
We revisit the classical problem of approximating a stochastic differential equation by a discrete-time and discrete-space Markov chain. Our construction iterates Caratheodory's theorem over time to match the moments of the increments locally. This allows to construct a Markov chain with a spar...
| Main Authors: | , , |
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| Format: | Internet publication |
| Language: | English |
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2021
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| _version_ | 1826310053884329984 |
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| author | Cosentino, F Oberhauser, H Abate, A |
| author_facet | Cosentino, F Oberhauser, H Abate, A |
| author_sort | Cosentino, F |
| collection | OXFORD |
| description | We revisit the classical problem of approximating a stochastic differential equation by a discrete-time and discrete-space Markov chain. Our construction iterates Caratheodory's theorem over time to match the moments of the increments locally. This allows to construct a Markov chain with a sparse transition matrix where the number of attainable states grows at most polynomially as time increases. Moreover, the MC evolves on a tree whose nodes lie on a "universal lattice" in the sense that an arbitrary number of different SDEs can be approximated on the same tree. The construction is not tailored to specific models, we discuss both the case of uni-variate and multi-variate case SDEs, and provide an implementation and numerical experiments. |
| first_indexed | 2024-03-07T07:44:52Z |
| format | Internet publication |
| id | oxford-uuid:0acafe5c-0280-4c2d-aed2-4d9c3332e84f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:44:52Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | oxford-uuid:0acafe5c-0280-4c2d-aed2-4d9c3332e84f2023-06-09T09:34:15ZMarkov chain approximations to stochastic differential equations by recombination on lattice treesInternet publicationhttp://purl.org/coar/resource_type/c_7ad9uuid:0acafe5c-0280-4c2d-aed2-4d9c3332e84fEnglishSymplectic Elements2021Cosentino, FOberhauser, HAbate, AWe revisit the classical problem of approximating a stochastic differential equation by a discrete-time and discrete-space Markov chain. Our construction iterates Caratheodory's theorem over time to match the moments of the increments locally. This allows to construct a Markov chain with a sparse transition matrix where the number of attainable states grows at most polynomially as time increases. Moreover, the MC evolves on a tree whose nodes lie on a "universal lattice" in the sense that an arbitrary number of different SDEs can be approximated on the same tree. The construction is not tailored to specific models, we discuss both the case of uni-variate and multi-variate case SDEs, and provide an implementation and numerical experiments. |
| spellingShingle | Cosentino, F Oberhauser, H Abate, A Markov chain approximations to stochastic differential equations by recombination on lattice trees |
| title | Markov chain approximations to stochastic differential equations by recombination on lattice trees |
| title_full | Markov chain approximations to stochastic differential equations by recombination on lattice trees |
| title_fullStr | Markov chain approximations to stochastic differential equations by recombination on lattice trees |
| title_full_unstemmed | Markov chain approximations to stochastic differential equations by recombination on lattice trees |
| title_short | Markov chain approximations to stochastic differential equations by recombination on lattice trees |
| title_sort | markov chain approximations to stochastic differential equations by recombination on lattice trees |
| work_keys_str_mv | AT cosentinof markovchainapproximationstostochasticdifferentialequationsbyrecombinationonlatticetrees AT oberhauserh markovchainapproximationstostochasticdifferentialequationsbyrecombinationonlatticetrees AT abatea markovchainapproximationstostochasticdifferentialequationsbyrecombinationonlatticetrees |