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On a class of martingale problems on Banach spaces

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2013

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https://doi.org/10.1214/EJP.v18-2924
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Electronic Journal of Probability. 2013, 18, 104. eISSN 1083-6489. Available under: doi: 10.1214/EJP.v18-2924

Zusammenfassung

We introduce the local martingale problem associated to semilinear stochastic evolution equations driven by a cylindrical Wiener process and establish a one-to-one correspondence between solutions of the martingale problem and (analytically) weak solutions of the stochastic equation. We also prove that the solutions of well-posed equations are strong Markov processes. We apply our results to semilinear stochastic equations with additive noise where the semilinear term is merely measurable and to stochastic reaction-diffusion equations with Hölder continuous multiplicative noise.

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Fachgebiet (DDC)
510 Mathematik

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Local Martingale problem; Strong Markov property; Stochastic partial differential equations

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ISO 690KUNZE, Markus, 2013. On a class of martingale problems on Banach spaces. In: Electronic Journal of Probability. 2013, 18, 104. eISSN 1083-6489. Available under: doi: 10.1214/EJP.v18-2924
BibTex
@article{Kunze2013class-41251,
  year={2013},
  doi={10.1214/EJP.v18-2924},
  title={On a class of martingale problems on Banach spaces},
  volume={18},
  journal={Electronic Journal of Probability},
  author={Kunze, Markus},
  note={Article Number: 104}
}
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