Stratonovich integral – Knowledge and References

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Diffusion processes, stochastic differential equations and applications

Published in Henry C. Tuckwell, Elementary Applications of Probability Theory, 2018

As mentioned in the last section, the approach we have used has the apparent drawback of necessitating a choice of stochastic integral. Fortunately, however, in this case the derivation of a diffusion approximation to Malthusian growth has been carried out (Tuckwell and Walsh, 1983a) from first principles. This approximation satisfies Equation (12.35) interpreted as a Stratonovich equation. Note that this does not imply that the Stratonovich integral is better or more correct than the Ito integral.

The backward problem of a stochastic PDE with bi-harmonic operator driven by fractional Brownian motion

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Journal Information

Published in Applicable Analysis, 2022

Xiaoli Feng, Chen Chen

Noting that the fBm is not continuous about the parameter H. When , the stochastic integral is in the sense of the Skorohod integral. While , the stochastic integral is the Itô integral. If letting , the stochastic integral will tend to the Stratonovich integral but not the Itô integral. Therefore, if letting , (12) cannot coincide with (13). One can refer to Ref. [39] for more in detail.