The stochastic integral of noncausal type as an extension of the symmetric integrals. (English) Zbl 0616.60056
In a previous paper ”Quelques propriétés de l’integrale stochastique du type noncausal.” ibid. 1, 405-416 (1984) the author had defined a stochastic integral with respect to Brownian motion based on orthogonal expansion of Brownian paths. He showed that this integral, which he calls ”of noncausal type” contains the integral of Stratonovich-Fisk as a special case.
In the present paper he continues research on this integral showing that it also contains another symmetric integral previously introduced by the author [Proc. Japan Acad. 46, 153-157 (1970; Zbl 0209.486)]. To this end he characterizes those orthonormal systems that make every quasi- martingale integrable (for the new integral).
In the present paper he continues research on this integral showing that it also contains another symmetric integral previously introduced by the author [Proc. Japan Acad. 46, 153-157 (1970; Zbl 0209.486)]. To this end he characterizes those orthonormal systems that make every quasi- martingale integrable (for the new integral).
Reviewer: G.Ritter
Keywords:
orthogonal expansion of Brownian paths; integral of Stratonovich-Fisk; symmetric integral; quasi-martingaleCitations:
Zbl 0209.486References:
| [1] | H. P. McKean, Stochastic Integrals, Academic Press, New York, 1969. |
| [2] | S. Ogawa, Quelques propriétés de l’intégrale stochastique du type noncausal. Japan J. Appl. Math.,1 (1984), 405–416. · Zbl 0633.60076 · doi:10.1007/BF03167066 |
| [3] | S. Ogawa, On a Riemann definition of the stochastic integral, (I), (II). Proc. Japan Acad.,46 (1970), 153–161. · Zbl 0209.48605 · doi:10.3792/pja/1195520461 |
| [4] | S. Ogawa, Remarks on theB-shifts of generalized random functions. Proc. Intern. Symposium on S.D.E. Kyoto, Kinokuniya Book-Store Co., Ltd., Tokyo, 1976. |
| [5] | S. Ogawa, Une remarque sur l’approximation de l’intégrale stochastique du type noncausal par une suite des intégrales de Stieltjes. Tôhoku Math. J.,36 (1984), 41–48. · Zbl 0551.60058 · doi:10.2748/tmj/1178228902 |
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