On the Identification of Noncausal Wiener Functionals from the Stochastic Fourier Coefficients

Kiyoiki Hoshino1, Tetsuya Kazumi1
1Graduate School of Science, Osaka Prefecture University, Sakai, Japan

Tóm tắt

Từ khóa


Tài liệu tham khảo

Hoshino, K., Kazumi, T.: On the Ogawa integrability of noncausal Wiener functionals, preprint (2017)

Itõ, K.: Stochastic integral. Proc. Imp. Acad. Tokyo 20, 519–524 (1944)

Itõ, K.: Multiple Wiener integral. J. Math. Soc. Jpn. 3, 157–169 (1951)

Ogawa, S.: Sur le produit direct du bruit blanc par lui-même. C. R. Acad. Sc. Paris Sér. A 288, 359–362 (1979)

Ogawa, S.: Quelques propriétés de l’intégrale stochastique du type noncausal. Jpn. J. Appl. Math. 1, 405–416 (1984)

Ogawa, S.: Une remarque sur l’approximation de l’intégrale stochastique du type noncausal par une suite des intégrales de Stieltjes. Tohoku Math. J. (2) 36(1), 41–48 (1984)

Ogawa, S.: The stochastic integral of noncausal type as an extension of the symmetric integrals. Jpn. J. Appl. Math. 2, 229–240 (1985)

Ogawa, S.: On the stochastic integral equation of Fredholm type. In: Patterns and Waves (monograph). Stud. Math. Appl. Kinokuniya 18, 597–606 (1986)

Ogawa, S.: Stochastic integral equations for the random fields. Semin. Probl. XXV, 324–339 (1991)

Ogawa, S.: On a stochastic Fourier transformation. Stochastics 85, 286–294 (2013)

Ogawa, S.: A direct inversion formula for the SFT. Sankhya A 77, 30–45 (2015)

Ogawa, S., Uemura, H.: On a stochastic Fourier coefficient: case of noncausal functions. J. Theor. Probab. 27, 370–382 (2014)

Ogawa, S., Uemura, H.: Identification of a noncausal Itõ process from the stochastic Fourier coefficients. Bull. Sci. Math. 138, 147–163 (2014)

Ogawa, S., Uemura, H.: On the identification of noncausal functions from the SFCs. RIMS Kôkyûroku 1952, 128–134 (2015)

Skorokhod, A.V.: On a generalization of a stochastic integral. Theory Probab. Appl. 20, 219–233 (1975)