Adapted integral representations of random variables
2015 ◽
Vol 36
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pp. 1560004
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Keyword(s):
We study integral representations of random variables with respect to general Hölder continuous processes and with respect to two particular cases; fractional Brownian motion and mixed fractional Brownian motion. We prove that an arbitrary random variable can be represented as an improper integral, and that the stochastic integral can have any distribution. If in addition the random variable is a final value of an adapted Hölder continuous process, then it can be represented as a proper integral. It is also shown that in the particular case of mixed fractional Brownian motion, any adapted random variable can be represented as a proper integral.
2019 ◽
Vol 522
◽
pp. 215-231
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2019 ◽
Vol 2019
(1)
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2018 ◽
Vol 1097
◽
pp. 012081
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2017 ◽
Vol 35
(6)
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pp. 943-953
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2020 ◽
Vol 555
◽
pp. 124458
◽