@article{EJP468,
author = {Chunrong Feng and Huaizhong Zhao},
title = {A Generalized Ito's Formula in Two-Dimensions and Stochastic Lebesgue-Stieltjes Integrals},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {12},
year = {2007},
keywords = {local time; continuous semimartingale; generalized It\$hat \{rm o\}\$'s formula; stochastic Lebesgue-Stieltjes integral},
abstract = {In this paper, a generalized It${\hat {\rm o}}$'s formula for continuous functions of two-dimensional continuous semimartingales is proved. The formula uses the local time of each coordinate process of the semimartingale, the left space first derivatives and the second derivative $\nabla _1^- \nabla _2^-f$, and the stochastic Lebesgue-Stieltjes integrals of two parameters. The second derivative $\nabla _1^- \nabla _2^-f$ is only assumed to be of locally bounded variation in certain variables. Integration by parts formulae are asserted for the integrals of local times. The two-parameter integral is defined as a natural generalization of both the Ito integral and the Lebesgue-Stieltjes integral through a type of It${\hat {\rm o }}$ isometry formula.},
pages = {no. 57, 1568-1599},
issn = {1083-6489},
doi = {10.1214/EJP.v12-468},
url = {http://ejp.ejpecp.org/article/view/468}}