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Asymptotic expansions in limit theorems for stochastic processes. – III
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  • Published: 04 November 2003

Asymptotic expansions in limit theorems for stochastic processes. – III

  • Alexander D. Wentzell1 

Probability Theory and Related Fields volume 128, pages 63–81 (2004)Cite this article

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Abstract.

For families of processes with independent increments ηɛ(t), 0≤t≤T, with frequent small jumps, limit theorems for expectations of the functionals F(ηɛ[0, T]) are proved of the form where diD , are positive numbers, A di are linear integro-differential or differential operators acting on functionals, and some differentiability conditions are imposed on the functional F. The case of power ‘tails’ of the jump distribution is considered.

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Authors and Affiliations

  1. Department of Mathematics, Tulane University, New Orleans, LA 70118, USA

    Alexander D. Wentzell

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  1. Alexander D. Wentzell
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Mathematics Subject Classification (2000): 60F17

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Wentzell, A. Asymptotic expansions in limit theorems for stochastic processes. – III. Probab. Theory Relat. Fields 128, 63–81 (2004). https://doi.org/10.1007/s00440-003-0294-y

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  • Received: 26 March 2003

  • Revised: 03 August 2003

  • Published: 04 November 2003

  • Issue Date: January 2004

  • DOI: https://doi.org/10.1007/s00440-003-0294-y

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Keywords

  • Stochastic Process
  • Differential Operator
  • Asymptotic Expansion
  • Limit Theorem
  • Independent Increment
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