Stochastic differential equations driven by processes generated by divergence form operators II: convergence results

Antoine Lejay

ESAIM: Probability and Statistics (2008)

  • Volume: 12, page 387-411
  • ISSN: 1292-8100

Abstract

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We have seen in a previous article how the theory of “rough paths” allows us to construct solutions of differential equations driven by processes generated by divergence form operators. In this article, we study a convergence criterion which implies that one can interchange the integral with the limit of a family of stochastic processes generated by divergence form operators. As a corollary, we identify stochastic integrals constructed with the theory of rough paths with Stratonovich or Itô integrals already constructed for stochastic processes generated by divergence form operators by using time-reversal techniques.

How to cite

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Lejay, Antoine. "Stochastic differential equations driven by processes generated by divergence form operators II: convergence results." ESAIM: Probability and Statistics 12 (2008): 387-411. <http://eudml.org/doc/250413>.

@article{Lejay2008,
abstract = { We have seen in a previous article how the theory of “rough paths” allows us to construct solutions of differential equations driven by processes generated by divergence form operators. In this article, we study a convergence criterion which implies that one can interchange the integral with the limit of a family of stochastic processes generated by divergence form operators. As a corollary, we identify stochastic integrals constructed with the theory of rough paths with Stratonovich or Itô integrals already constructed for stochastic processes generated by divergence form operators by using time-reversal techniques. },
author = {Lejay, Antoine},
journal = {ESAIM: Probability and Statistics},
keywords = {Rough paths; stochastic differential equations; stochastic process generated by divergence form operators; Condition UTD; convergence of stochastic integrals; rough paths; stochastic process generated by divergence form operators; condition UTD},
language = {eng},
month = {7},
pages = {387-411},
publisher = {EDP Sciences},
title = {Stochastic differential equations driven by processes generated by divergence form operators II: convergence results},
url = {http://eudml.org/doc/250413},
volume = {12},
year = {2008},
}

TY - JOUR
AU - Lejay, Antoine
TI - Stochastic differential equations driven by processes generated by divergence form operators II: convergence results
JO - ESAIM: Probability and Statistics
DA - 2008/7//
PB - EDP Sciences
VL - 12
SP - 387
EP - 411
AB - We have seen in a previous article how the theory of “rough paths” allows us to construct solutions of differential equations driven by processes generated by divergence form operators. In this article, we study a convergence criterion which implies that one can interchange the integral with the limit of a family of stochastic processes generated by divergence form operators. As a corollary, we identify stochastic integrals constructed with the theory of rough paths with Stratonovich or Itô integrals already constructed for stochastic processes generated by divergence form operators by using time-reversal techniques.
LA - eng
KW - Rough paths; stochastic differential equations; stochastic process generated by divergence form operators; Condition UTD; convergence of stochastic integrals; rough paths; stochastic process generated by divergence form operators; condition UTD
UR - http://eudml.org/doc/250413
ER -

References

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