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Another approach to Brownian motion

Author

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  • Peligrad, Magda
  • Utev, Sergey

Abstract

Motivated by the central limit theorem for weakly dependent variables, we show that the Brownian motion {X(t);t[set membership, variant][0,1]}, can be modeled as a process with independent increments, satisfying the following limiting condition.almost surely for all 0[less-than-or-equals, slant]s 0, p[set membership, variant][1,2), A>0 and B,C[greater-or-equal, slanted]0).

Suggested Citation

  • Peligrad, Magda & Utev, Sergey, 2006. "Another approach to Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 279-292, February.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:2:p:279-292
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    References listed on IDEAS

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    1. Jakubowski, Adam, 1993. "Minimal conditions in p-stable limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 44(2), pages 291-327, February.
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