References
- K. Hoshino, Ogawa integrability of noncausal Wiener functionals and the identification of noncausal Wiener functionals from its SFCs (in Japanese), Master thesis, Osaka Prefecture University, 2017.
- P. Malliavin and M.E. Mancino, Fourier series method for measurement of multivariate volatilities, Finance Stoch. 6(1) (2002), pp. 49–61. doi: 10.1007/s780-002-8400-6
- P. Malliavin and A. Thalmaier, Stochastic Calculus of Variations in Mathematical Finance, Springer-Verlag, Berlin, 2009.
- S. Ogawa, Sur le produit direct du bruit blanc par lui-même, C. R. Acad. Sci. Série A 288 (1979), pp. 359–362.
- S. Ogawa, Quelques propriétés de l'integral stochastique du type noncausal, Japan J. Appl. Math. 1(2) (1984), pp. 405–416. doi: 10.1007/BF03167066
- S. Ogawa, On the Stochastic Integral Equation of Fredholm type, Patterns and Waves (monograph), Studies in Math. and Its Appl. Vol. 18, Elsevier, North-Holland, 1986, pp. 597–606.
- S. Ogawa, On a Stochastic Integral Equation for the Random Fields, Séminaire de Probabilités, Vol. XXV. Lecture Notes in Mathematics, Vol. 1485, Springer, Berlin, 1991, pp. 324–329.
- S. Ogawa, On a stochastic Fourier transformation, Stochastics 85(2) (2013), pp. 286–294. doi: 10.1080/17442508.2011.651621
- S. Ogawa, A direct inversion formula for the SFT, Sankhya A 77(1) (2015), pp. 30–45. doi: 10.1007/s13171-014-0056-1
- S. Ogawa, Noncausal Stochastic Calculus, Springer, Japan KK, 2017.
- S. Ogawa, Direct inversion formulas for the natural SFT, Sankhya A 80 (2018), pp. 267–279. doi:10.1007/s13171-018-0128-8
- S. Ogawa and H. Uemura, Identification of noncausal Itô processes from the stochastic Fourier coefficients, Bull. Sci. Math. 138(1) (2014), pp. 147–163. doi: 10.1016/j.bulsci.2013.12.003
- S. Ogawa and H. Uemura, Identification of noncausal Itô processes from the stochastic Fourier coefficients II, preprint (2016). Available at arXiv:1603.09486.
- S. Ogawa and H. Uemura, On a stochastic Fourier coefficient: Case of noncausal functions, J. Theor. Probab. 27(2) (2014), pp. 370–382. doi: 10.1007/s10959-012-0464-x
- S. Ogawa and H. Uemura, On the identification of noncausal functions from the SFCs, RIMS Kôkyûroku 1952 (2015), pp. 128–134.
- S. Ogawa and H. Uemura, Some aspects of strong inversion formulas of an SFT, Japan J. Indust. Appl. Math. 35(1) (2018), pp. 373–390. doi: 10.1007/s13160-017-0295-3
- A.V. Skorokhod, On a generalization of a stochastic integral, Theory Probab. Appl. 20(2) (1975), pp. 219–233. doi: 10.1137/1120030