Rough stochastic differential equations
2021
A hybrid theory of rough stochastic analysis is built. It seamlessly combines the advantages of both Ito's stochastic - and Lyons' rough differential equations. Well-posedness of rough stochastic differential equation is obtained, under natural assumptions and with precise estimates; many examples and applications are mentioned. A major role is played by a new stochastic variant of Gubinelli's controlled rough paths spaces, with norms that reflect some generalized stochastic sewing lemma, and which may prove useful whenever rough paths and Ito integration meet.
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