On the possibility of defining the Chapman–Kolmogorov semi-group on L∞
1979 ◽
Vol 83
(3-4)
◽
pp. 327-331
Keyword(s):
SynopsisIf the diffusion matrix coefficient of an Itô stochastic differential equation is everywhere non-singular, then the corresponding Chapman-Kolmogorov semi-group may be defined on L∼(Rn), the space of Lebesgue equivalence classes of essentially bounded Borei measurable functions. However, if the diffusion matrix is singular at some points of Rn, it is not clear that this can always be done. We show that in certain situations it is possible to do so.
2016 ◽
Vol 21
(6)
◽
pp. 751-769
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2008 ◽
Vol 40
(7)
◽
pp. 1-8
2020 ◽
Vol 28
(3)
◽
pp. 183-196