Il’chenko, S. A.; Mishura, U. S. Generalized integrals for random fields. (Ukrainian, English) Zbl 1050.60052 Teor. Jmovirn. Mat. Stat. 67, 57-70 (2002); translation in Theory Probab. Math. Stat. 67, 63-78 (2003). The authors propose the notion and construction of the forward and backward integrals for 2-parameter fields. Their approach is an extension of an analogous construction due to F. Russo and P. Vallois [Probab. Theory Relat. Fields 97, No. 3, 403–421 (1993; Zbl 0792.60046)]. The main properties of the proposed integrals are investigated; in particular, Itô’s formula is proved. Examples of calculating both forward and backward integrals for certain types of random fields, namely, semimartingales on the plane, fractional Brownian fields, fields with zero energy, are presented. Reviewer: N. M. Zinchenko (Kyïv) MSC: 60G60 Random fields 60H05 Stochastic integrals Keywords:stochastic integral; forward and backward integral; semimartingale; fractional Brownian field; field with zero energy Citations:Zbl 0792.60046 PDFBibTeX XMLCite \textit{S. A. Il'chenko} and \textit{U. S. Mishura}, Teor. Ĭmovirn. Mat. Stat. 67, 57--70 (2002; Zbl 1050.60052); translation in Theory Probab. Math. Stat. 67, 63--78 (2003)