Summary
A nonstandard construction of Lévy Brownian motion on ℝd is presented, which extends R.M. Anderson's nonstandard representation of Brownian motion. It involves a nonstandard construction of white noise and gives as a classical corollary a new white noise integral representation of Lévy Brownian motion. Moreover, a new invariance principle can be deduced in a similar way as Donsker's invariance principles follows from Anderson's construction.
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Stoll, A. A nonstandard construction of Lévy Brownian motion. Probab. Th. Rel. Fields 71, 321–334 (1986). https://doi.org/10.1007/BF01000208
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DOI: https://doi.org/10.1007/BF01000208
Keywords
- Stochastic Process
- Brownian Motion
- White Noise
- Probability Theory
- Integral Representation