Backward problems for stochastic differential equations on the Sierpinski gasket
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| _version_ | 1866910639141683200 |
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| author | Liu, Xuan Qian, Zhongmin |
| author_facet | Liu, Xuan Qian, Zhongmin |
| contents | In this paper, we study the non-linear backward problems (with deterministic or stochastic durations) of stochastic differential equations on the Sierpinski gasket. We prove the existence and uniqueness of solutions of backward stochastic differential equations driven by Brownian martingale (defined in Section [sec:-1]) on the Sierpinski gasket constructed by S. Goldstein and S. Kusuoka. The exponential integrability of quadratic processes for martingale additive functionals is obtained, and as an application, a Feynman-Kac representation formula for weak solutions of semi-linear parabolic PDEs on the gasket is also established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1612_01297 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Backward problems for stochastic differential equations on the Sierpinski gasket Liu, Xuan Qian, Zhongmin Probability 28A80, 60H10, 60H30 In this paper, we study the non-linear backward problems (with deterministic or stochastic durations) of stochastic differential equations on the Sierpinski gasket. We prove the existence and uniqueness of solutions of backward stochastic differential equations driven by Brownian martingale (defined in Section [sec:-1]) on the Sierpinski gasket constructed by S. Goldstein and S. Kusuoka. The exponential integrability of quadratic processes for martingale additive functionals is obtained, and as an application, a Feynman-Kac representation formula for weak solutions of semi-linear parabolic PDEs on the gasket is also established. |
| title | Backward problems for stochastic differential equations on the Sierpinski gasket |
| topic | Probability 28A80, 60H10, 60H30 |
| url | https://arxiv.org/abs/1612.01297 |