In this chapter, we will consider continuous semimartingales and show that stochastic differential equations driven by these can be analysed essentially using the same techniques as in the case of SDE driven by Brownian motion. This can be done using random time change. The use of random time change in study of solutions to stochastic differential equations was introduced in Karandikar, pathwise stochastic calculus of continuous semimartingales, 1981, , Karandikar, Sankhya A, 43:121–132, 1981, .
Karandikar, R. L., & Rao, B. V. (2018). Continuous Semimartingales. In Indian Statistical Institute Series (pp. 221–249). Springer Science and Business Media B.V. https://doi.org/10.1007/978-981-10-8318-1_7