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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.00733 |
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| _version_ | 1866915222205235200 |
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| author | Bardina, Xavier Boukfal, Salim |
| author_facet | Bardina, Xavier Boukfal, Salim |
| contents | In this paper we provide sufficient conditions for sequences of stochastic processes of the form $\int_{[0,t]} f_n(u) θ_n(u) du$, to weakly converge, in the space of continuous functions over a closed interval, to integrals with respect to the Brownian motion, $\int_{[0,t]} f(u)W(du)$, where $\{f_n\}_n$ is a sequence satisfying some integrability conditions converging to $f$ and $\{θ_n\}_n$ is a sequence of stochastic processes whose integrals $\int_{[0,t]}θ_n(u)du$ converge in law to the Brownian motion (in the sense of the finite dimensional distribution convergence), in the multidimensional parameter set case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00733 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak convergence of stochastic integrals Bardina, Xavier Boukfal, Salim Probability 60H05, 60F17 In this paper we provide sufficient conditions for sequences of stochastic processes of the form $\int_{[0,t]} f_n(u) θ_n(u) du$, to weakly converge, in the space of continuous functions over a closed interval, to integrals with respect to the Brownian motion, $\int_{[0,t]} f(u)W(du)$, where $\{f_n\}_n$ is a sequence satisfying some integrability conditions converging to $f$ and $\{θ_n\}_n$ is a sequence of stochastic processes whose integrals $\int_{[0,t]}θ_n(u)du$ converge in law to the Brownian motion (in the sense of the finite dimensional distribution convergence), in the multidimensional parameter set case. |
| title | Weak convergence of stochastic integrals |
| topic | Probability 60H05, 60F17 |
| url | https://arxiv.org/abs/2504.00733 |