# A Generalized Backward Equation For One Dimensional Processes

@article{Lowther2008AGB, title={A Generalized Backward Equation For One Dimensional Processes}, author={George Lowther}, journal={arXiv: Probability}, year={2008} }

Suppose that a real valued process X is given as a solution to a stochastic differential equation. Then, for any twice continuously differentiable function f, the backward Kolmogorov equation gives a condition for f(t,X) to be a local martingale.
We generalize the backward equation in two main ways. First, it is extended to non-differentiable functions. Second, the process X is not required to satisfy an SDE. Instead, it is only required to be a quasimartingale satisfying an integrability…

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