Wasserstein distance estimates for stochastic integrals by forward-backward stochastic calculus
We prove Wasserstein distance bounds between the probability distributions of stochastic integrals with jumps, based on the integrands appearing in their stochastic integral representations. Our approach does not rely on the Stein equation or on the propagation of convexity property for Markovian se...
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2022
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| Online Access: | https://hdl.handle.net/10356/160989 |
| _version_ | 1826128487184859136 |
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| author | Breton, Jean-Christophe Privault, Nicolas |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Breton, Jean-Christophe Privault, Nicolas |
| author_sort | Breton, Jean-Christophe |
| collection | NTU |
| description | We prove Wasserstein distance bounds between the probability distributions of stochastic integrals with jumps, based on the integrands appearing in their stochastic integral representations. Our approach does not rely on the Stein equation or on the propagation of convexity property for Markovian semigroups, and makes use instead of forward-backward stochastic calculus arguments. This allows us to consider a large class of target distributions constructed using Brownian stochastic integrals and pure jump martingales, which can be specialized to infinitely divisible target distributions with finite Lévy measure and Gaussian components. |
| first_indexed | 2024-10-01T07:25:44Z |
| format | Journal Article |
| id | ntu-10356/160989 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:25:44Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1609892022-08-10T08:04:36Z Wasserstein distance estimates for stochastic integrals by forward-backward stochastic calculus Breton, Jean-Christophe Privault, Nicolas School of Physical and Mathematical Sciences Science::Mathematics Wasserstein Distance Stochastic Integrals We prove Wasserstein distance bounds between the probability distributions of stochastic integrals with jumps, based on the integrands appearing in their stochastic integral representations. Our approach does not rely on the Stein equation or on the propagation of convexity property for Markovian semigroups, and makes use instead of forward-backward stochastic calculus arguments. This allows us to consider a large class of target distributions constructed using Brownian stochastic integrals and pure jump martingales, which can be specialized to infinitely divisible target distributions with finite Lévy measure and Gaussian components. Ministry of Education (MOE) This research is supported by the Ministry of Education, Singapore, under its Tier 2 Grant MOE2016-T2-1-036, and by the French government under its program ANR-11-LABX-0020-01 “Investissements d’Avenir”. 2022-08-10T08:04:36Z 2022-08-10T08:04:36Z 2022 Journal Article Breton, J. & Privault, N. (2022). Wasserstein distance estimates for stochastic integrals by forward-backward stochastic calculus. Potential Analysis, 56(1), 1-20. https://dx.doi.org/10.1007/s11118-020-09874-0 0926-2601 https://hdl.handle.net/10356/160989 10.1007/s11118-020-09874-0 2-s2.0-85089962363 1 56 1 20 en MOE2016-T2-1-036 Potential Analysis © 2020 Springer Nature B.V. All rights reserved. |
| spellingShingle | Science::Mathematics Wasserstein Distance Stochastic Integrals Breton, Jean-Christophe Privault, Nicolas Wasserstein distance estimates for stochastic integrals by forward-backward stochastic calculus |
| title | Wasserstein distance estimates for stochastic integrals by forward-backward stochastic calculus |
| title_full | Wasserstein distance estimates for stochastic integrals by forward-backward stochastic calculus |
| title_fullStr | Wasserstein distance estimates for stochastic integrals by forward-backward stochastic calculus |
| title_full_unstemmed | Wasserstein distance estimates for stochastic integrals by forward-backward stochastic calculus |
| title_short | Wasserstein distance estimates for stochastic integrals by forward-backward stochastic calculus |
| title_sort | wasserstein distance estimates for stochastic integrals by forward backward stochastic calculus |
| topic | Science::Mathematics Wasserstein Distance Stochastic Integrals |
| url | https://hdl.handle.net/10356/160989 |
| work_keys_str_mv | AT bretonjeanchristophe wassersteindistanceestimatesforstochasticintegralsbyforwardbackwardstochasticcalculus AT privaultnicolas wassersteindistanceestimatesforstochasticintegralsbyforwardbackwardstochasticcalculus |