# Stochastic viability and a comparison theorem

Colloquium Mathematicae (1995)

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

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topMilian, 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

top- [1] J.-P. Aubin, Viability theory, to appear. Zbl1179.93001
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- [4] J.-P. Aubin and G. Da Prato, Stochastic Nagumo's viability theorem, Cahiers de Mathématiques de la Décision 9224, CEREMADE. Zbl0816.60053
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- [8] S. Gautier and L. Thibault, Viability for constrained stochastic differential equations, Differential and Integral Equations 6 (1993), 1395-1414. Zbl0780.93085
- [9] I. I. Gihman and A. V. Skorohod, Stochastic Differential Equations, Springer, 1972. Zbl0242.60003
- [10] N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, 1981. Zbl0495.60005
- [11] D. Isaacson, Stochastic integrals and derivatives, Ann. Math. Statist. 40 (1969), 1610-1616. Zbl0181.43504
- [12] A. Milian, A note on the stochastic invariance for Itô equations, Bull. Polish Acad. Sci. Math. 41 (1993), 139-150. Zbl0796.60071
- [13] B. N. Pshenichnyĭ, Convex Analysis and Extremal Problems, Nauka, Moscow, 1980 (in Russian). Zbl0477.90034
- [14] J. T. Schwartz, Nonlinear Functional Analysis, Courant Inst. Math. 1965.
- [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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