Stochastic viability and a comparison theorem

Anna Milian

Colloquium Mathematicae (1995)

  • Volume: 68, Issue: 2, page 297-316
  • ISSN: 0010-1354

Abstract

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We give explicit necessary and sufficient conditions for the viability of polyhedrons with respect to Itô equations. Using the viability criterion we obtain a comparison theorem for multi-dimensional Itô processes

How to cite

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Milian, Anna. "Stochastic viability and a comparison theorem." Colloquium Mathematicae 68.2 (1995): 297-316. <http://eudml.org/doc/210314>.

@article{Milian1995,
abstract = {We give explicit necessary and sufficient conditions for the viability of polyhedrons with respect to Itô equations. Using the viability criterion we obtain a comparison theorem for multi-dimensional Itô processes},
author = {Milian, Anna},
journal = {Colloquium Mathematicae},
keywords = {Itô equation; Wiener process; stochastic viability for a convex polyhedron; comparison theorems},
language = {eng},
number = {2},
pages = {297-316},
title = {Stochastic viability and a comparison theorem},
url = {http://eudml.org/doc/210314},
volume = {68},
year = {1995},
}

TY - JOUR
AU - Milian, Anna
TI - Stochastic viability and a comparison theorem
JO - Colloquium Mathematicae
PY - 1995
VL - 68
IS - 2
SP - 297
EP - 316
AB - We give explicit necessary and sufficient conditions for the viability of polyhedrons with respect to Itô equations. Using the viability criterion we obtain a comparison theorem for multi-dimensional Itô processes
LA - eng
KW - Itô equation; Wiener process; stochastic viability for a convex polyhedron; comparison theorems
UR - http://eudml.org/doc/210314
ER -

References

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  2. [2] J.-P. Aubin and A. Cellina, Differential Inclusions, Springer, 1984. Zbl0538.34007
  3. [3] J.-P. Aubin and G. Da Prato, Stochastic viability and invariance, Ann. Scuola Norm. Sup. Pisa 27 (1990), 595-694. 
  4. [4] J.-P. Aubin and G. Da Prato, Stochastic Nagumo's viability theorem, Cahiers de Mathématiques de la Décision 9224, CEREMADE. Zbl0816.60053
  5. [5] K. Borsuk, Multidimensional Analytic Geometry, PWN, 1969. 
  6. [6] R. Durrett, Brownian Motion and Martingales in Analysis, Wadsworth Adv. Books and Software, Wadsworth, Belmont, Calif., 1984. Zbl0554.60075
  7. [7] S. N. Ethier and T. G. Kurtz, Markov Processes. Characterization and Convergence, Wiley, 1986. Zbl0592.60049
  8. [8] S. Gautier and L. Thibault, Viability for constrained stochastic differential equations, Differential and Integral Equations 6 (1993), 1395-1414. Zbl0780.93085
  9. [9] I. I. Gihman and A. V. Skorohod, Stochastic Differential Equations, Springer, 1972. Zbl0242.60003
  10. [10] N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, 1981. Zbl0495.60005
  11. [11] D. Isaacson, Stochastic integrals and derivatives, Ann. Math. Statist. 40 (1969), 1610-1616. Zbl0181.43504
  12. [12] A. Milian, A note on the stochastic invariance for Itô equations, Bull. Polish Acad. Sci. Math. 41 (1993), 139-150. Zbl0796.60071
  13. [13] B. N. Pshenichnyĭ, Convex Analysis and Extremal Problems, Nauka, Moscow, 1980 (in Russian). Zbl0477.90034
  14. [14] J. T. Schwartz, Nonlinear Functional Analysis, Courant Inst. Math. 1965. 
  15. [15] C. Yoerp, Sur la dérivation des intégrales stochastiques, in: Sém. Probab. XV, Lecture Notes in Math. 784, Springer, 1980, 249-253. 

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