Summary.
Let (W, H, μ) be an abstract Wiener space and let Tw = w + u (w), where u is an H-valued random variable, be a measurable transformation on W. A Sard type lemma and a degree theorem for this setup are presented and applied to derive existence of solutions to elliptic stochastic partial differential equations.
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Received: 19 March 1996 / In revised form: 7 January 1997
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Üstünel, A., Zakai, M. Degree theory on Wiener space. Probab Theory Relat Fields 108, 259–279 (1997). https://doi.org/10.1007/s004400050109
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DOI: https://doi.org/10.1007/s004400050109
- Mathematics Subject Classification (1991): 60G30
- 60H07
- 60H15
- 60H30
- 60B11
- 28C20
- 46G12