• Corpus ID: 18564769

A Generalized Backward Equation For One Dimensional Processes

  title={A Generalized Backward Equation For One Dimensional Processes},
  author={George Lowther},
  journal={arXiv: Probability},
  • G. Lowther
  • Published 23 March 2008
  • Mathematics
  • arXiv: Probability
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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