Stratonovich differential equations
Abstract
The Stratonovich integral is extended for functions of one dimensional semi-martingales $\sigma(X\sb{t}$), where $\sigma$ is absolutely continuous and its derivative has a version which is right continuous with left limit. Then, one dimensional Stratonovich differential equations are considered. A general theorem of existence (strong) is proved in Chapter II, moreover a maximal and a minimal solutions are constructed. In the next chapter the problem of uniqueness is studied, obtaining several results in this direction. In particular, in the Brownian case the problem is deeply studied. Finally, in the last chapter an explicit connection between ordinary differential equations and Stratonovich differential equations is made, generalizing the work of Doss.
Degree
Ph.D.
Advisors
Protter, Purdue University.
Subject Area
Statistics|Mathematics
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