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Weak convergence to the multiple Stratonovich integral

Author

Listed:
  • Bardina, Xavier
  • Jolis, Maria

Abstract

We have considered the problem of the weak convergence, as [var epsilon] tends to zero, of the multiple integral processesin the space , where f[set membership, variant]L2([0,T]n) is a given function, and {[eta][var epsilon](t)}[var epsilon]>0 is a family of stochastic processes with absolutely continuous paths that converges weakly to the Brownian motion. In view of the known results when n[greater-or-equal, slanted]2 and f(t1,...,tn)=1{t1

Suggested Citation

  • Bardina, Xavier & Jolis, Maria, 2000. "Weak convergence to the multiple Stratonovich integral," Stochastic Processes and their Applications, Elsevier, vol. 90(2), pages 277-300, December.
    • Handle: RePEc:eee:spapps:v:90:y:2000:i:2:p:277-300
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    Citations

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    Cited by:

    1. Christophe Chorro, 2005. "Convergence en loi de Dirichlet de certaines intégrales stochastiques," Cahiers de la Maison des Sciences Economiques b05036, Université Panthéon-Sorbonne (Paris 1).
    2. Mirzaee, Farshid & Hadadiyan, Elham, 2017. "Solving system of linear Stratonovich Volterra integral equations via modification of hat functions," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 254-264.
    3. Christophe Chorro, 2005. "Convergence en loi de Dirichlet de certaines intégrales stochastiques," Post-Print halshs-00194673, HAL.
    4. Errami, Mohammed & Russo, Francesco, 2003. "n-covariation, generalized Dirichlet processes and calculus with respect to finite cubic variation processes," Stochastic Processes and their Applications, Elsevier, vol. 104(2), pages 259-299, April.
    5. Bardina, Xavier & Jolis, Maria & A. Tudor, Ciprian, 2003. "Convergence in law to the multiple fractional integral," Stochastic Processes and their Applications, Elsevier, vol. 105(2), pages 315-344, June.
    6. Jolis, Maria & Viles, Noèlia, 2007. "Continuity with respect to the Hurst parameter of the laws of the multiple fractional integrals," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1189-1207, September.

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