Weak Convergence of Stochastic Integrals and Differential Equations ∗

@inproceedings{Kurtz2004WeakCO,
  title={Weak Convergence of Stochastic Integrals and Differential Equations ∗},
  author={Thomas Kurtz and Philip Protter},
  year={2004}
}
Let W denote a standard Wiener process with W0 = 0. For a variety of reasons, it is desirable to have a notion of an integral ∫ 1 0 HsdWs, where H is a stochastic process; or more generally an indefinite integral ∫ t 0 HsdWs, 0 ≤ t < ∞. If H is a process with continuous paths, an obvious way to define a stochastic integral is by a limit of sums: let πn[0, t] be a sequence of partitions of [0, t], with mesh (πn) = supi(ti+1 − ti), where 0 = t0 < t1 < · · · < tn = t are the successive points of… CONTINUE READING
Highly Influential
This paper has highly influenced 11 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS

From This Paper

Topics from this paper.
42 Citations
15 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 15 references

Weak Limit Theorems for Stochastic Integrals and Stochastic Differential Equations

  • T. G. Kurtz, P. Protter
  • Ann. Proba
  • 1991
Highly Influential
8 Excerpts

Convergence en Loi des Suites d’Intégrales Stochastiques sur l’Espace D1 de Skorohod

  • A. Jakubowski, J. Mémin, G. Pagès
  • Proba. Th. Rel. Fields
  • 1989
Highly Influential
4 Excerpts

Stochastic Integration and Differential Equations, Springer, Berlin

  • P. Protter
  • 1990
Highly Influential
3 Excerpts

A Remark on Stochastic Integration

  • H. Ahn, P. Protter
  • Sém. de Proba. XXVII,
  • 1994
3 Excerpts

A Remark on the Weak Convergence of Processes in the Skorohod Topology

  • J. Jacod, P. Protter
  • J. Theoretical Probability,
  • 1993
2 Excerpts

Characterizing the Weak Convergence of Stochastic Integrals”, in Stochastic Analysis (M

  • T. G. Kurtz, P. Protter
  • 1991

Condition UT et Stabilité en Loi des Solutions d’Equations Différentielles Stochastiques

  • J. Mémin, L. Slominski
  • Sém. de Proba. XXV,
  • 1991

Wong-Zakai, Corrections, Random Evolutions, and Numerical Schemes for SDEs”, in Stochastic Analysis

  • T. G. Kurtz, P. Protter
  • 1991
1 Excerpt

On the Azéma Martingales

  • M. Emery
  • Sém. de Proba. XXIII,
  • 1989
2 Excerpts

Similar Papers

Loading similar papers…