Advanced search
Publication Cover
Stochastics and Stochastic Reports Volume 27, 1989 - Issue 4
Journal homepage
27
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Sample path properties of stochastic integrals, and stochastic differentiation

Martin T. Barlow Statistical Laboratory, 16 Mill Lane, Cambridge, UK CB2 1SB
&
Edwin A. Perkins Mathematics Department, University of British Columbia, Vancouver, B.C, Canada
Pages 261-293 | Received 24 May 1988, Published online: 04 Apr 2007

References

  • Barlow , M. T. 1988 . Skew Brownian motion and a one-dimensional stochastic differential equation . Stochastics , 25 : 1 – 2 .
  • Barlow , M. T. and Perkins , E. A. 1984 . Levels at which every Brownian excursion is exceptional, Sem Prob. . Lecture Notes in Mathematics 1059 , XVIII : 1 – 28 .
  • Barlow , M. T. and Perkins , E. A. 1986 . Brownian motion at a slow point . Trans. A.M.S , 296 : 741 – 775 .
  • Barlow , M. T. and Perkins , E. A. On pathwise uniqueness and expansion of filtrations , To appear
  • Davis , M. H. A. 1975 . On stochastic differentiation . Th. Prob. and Appl , 22 : 869 – 872 .
  • Freedman , D. 1975 . On tail probablities for martingales . Ann. Prob , 3 : 100 – 118 .
  • Greenwood , P. and Perkins , E. A. 1983 . A conditional limit theorem for random walk and Brownian local time on square root boundaries . Ann. Prob , 11 : 227 – 261 .
  • Hoover , D. N. and Perkins , E. A. 1983 . Nonstandard construction of the stochastic integral and applications to SDEs, I and II . Trans. Amer. Math. Soc , 275 : 58 – 36 .
  • Isaacson , D. 1969 . Stochastic integrals and derivatives . Ann. Math. Stat , 40 : 1610 – 1616 .
  • Jeulin , J. “ Semi-martingales et grossissement d'une filtration ” . In Lect. Notes Math. , Vol. 833 , Springer .
  • Keisler , H. J. 1984 . An infinitesimal approach to stochastic analysis . Mem. Amer. Math. Soc , 297
  • Knight , F. B. 1981 . Essentials of Brownian motion and diffusion . AMS Math. Surveys , 18 AMS, Providence, Rhode Island
  • LeGall , J.-F. 1983 . “ Applications du temps local aux equations differentielles stochastiques unidimension- elles, Sem. Prob. XVII ” . In Lect. Notes Math. , Vol. 986 , Berlin : Springer .
  • Nako , S. 1972 . On the pathwise uniqueness of solutions of stochastic differential equations . Osaka J. Math , 9 : 513 – 518 .
  • Pitman , J. W. 1975 . One-dimensional Brownian motion and the three-dimensional Bessel process . J. Appl. Prob , 7 : 511 – 526 .
  • Taylor , J. W. 1974 . Regularity of irregularities on a Brownian path . Ann. Inst. Fourier , 24 : 195 – 203 .
  • Williams , D. 1970 . Decomposing the Brownian path . Bull. Am. Math. Soc , 76 : 871 – 873 .
  • Cutland , D. 1983 . Nonstandard measure theory and its applications . Bull. LMS , 15 : 529 – 589 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Supercharge Your Next Research Paper: Research and write your next paper with Jenni AI.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.