| 1. | Sample paths of a Gaussian process with the exponential covariance function are not smooth.
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| 2. | :i . e ., all adapted processes with absolutely continuous sample paths.
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| 3. | Almost surely, a sample path of a Wiener process is continuous everywhere but nowhere differentiable.
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| 4. | This leads to a sample path of
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| 5. | Approximate sample paths of the Langevin diffusion can be generated by many discrete-time methods.
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| 6. | Instead of generating random paths, new sampling paths are created as slight mutations of existing ones.
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| 7. | A prevalent example of the controlled path X _ t is the sample path of a Wiener process.
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| 8. | This last characterization gives an understanding of the structure of the sample path with location and sizes of jumps.
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| 9. | An example of a continuous-time stochastic process for which sample paths are not continuous is a Poisson process.
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| 10. | The sample paths chosen can be thought of as showing discrete sampled points on an " fBm " process.
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