Summary
We study stochastic differential equations of the formdX t=σ(X t)dMt+b(Xt)d<M>t whereM is a continuous local martingale and <M> stands for its quadratic variation process. The conditions introduced by Engelbert and Schmidt, which ensure the existence and uniqueness in law of solutions of SDE's driven by the Wiener process without drift (or with generalized drift) are shown to be no longer valid.
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Rutkowski, M. On solutions of stochastic differential equations with drift. Probab. Th. Rel. Fields 85, 387–402 (1990). https://doi.org/10.1007/BF01193944
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DOI: https://doi.org/10.1007/BF01193944
Keywords
- Differential Equation
- Stochastic Process
- Probability Theory
- Variation Process
- Mathematical Biology