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

ESAIM: Probability and Statistics (2008)

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

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topLejay, 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 -

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