Deterministic characterization of viability for stochastic differential equation driven by fractional brownian motion

Tianyang Nie; Aurel Răşcanu

ESAIM: Control, Optimisation and Calculus of Variations (2012)

  • Volume: 18, Issue: 4, page 915-929
  • ISSN: 1292-8119

Abstract

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In this paper, using direct and inverse images for fractional stochastic tangent sets, we establish the deterministic necessary and sufficient conditions which control that the solution of a given stochastic differential equation driven by the fractional Brownian motion evolves in some particular sets K. As a consequence, a comparison theorem is obtained.

How to cite

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Nie, Tianyang, and Răşcanu, Aurel. "Deterministic characterization of viability for stochastic differential equation driven by fractional brownian motion." ESAIM: Control, Optimisation and Calculus of Variations 18.4 (2012): 915-929. <http://eudml.org/doc/272866>.

@article{Nie2012,
abstract = {In this paper, using direct and inverse images for fractional stochastic tangent sets, we establish the deterministic necessary and sufficient conditions which control that the solution of a given stochastic differential equation driven by the fractional Brownian motion evolves in some particular sets K. As a consequence, a comparison theorem is obtained.},
author = {Nie, Tianyang, Răşcanu, Aurel},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {stochastic viability; stochastic differential equation; stochastic tangent set; fractional brownian motion; fractional Brownian motion},
language = {eng},
number = {4},
pages = {915-929},
publisher = {EDP-Sciences},
title = {Deterministic characterization of viability for stochastic differential equation driven by fractional brownian motion},
url = {http://eudml.org/doc/272866},
volume = {18},
year = {2012},
}

TY - JOUR
AU - Nie, Tianyang
AU - Răşcanu, Aurel
TI - Deterministic characterization of viability for stochastic differential equation driven by fractional brownian motion
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2012
PB - EDP-Sciences
VL - 18
IS - 4
SP - 915
EP - 929
AB - In this paper, using direct and inverse images for fractional stochastic tangent sets, we establish the deterministic necessary and sufficient conditions which control that the solution of a given stochastic differential equation driven by the fractional Brownian motion evolves in some particular sets K. As a consequence, a comparison theorem is obtained.
LA - eng
KW - stochastic viability; stochastic differential equation; stochastic tangent set; fractional brownian motion; fractional Brownian motion
UR - http://eudml.org/doc/272866
ER -

References

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  7. [7] I. Ciotir and A. Rascanu, Viability for stochastic differential equation driven by fractional Brownian motions. J. Differential Equations247 (2009) 1505–1528. Zbl1168.60018MR2541419
  8. [8] B.B. Mandelbrot and J.W. Van Ness, Fractional Brownian motions, fractional noises and applications. SIAM Rev.10 (1968) 422–437. Zbl0179.47801MR242239
  9. [9] A. Milian, A note on stochastic invariance for Ito equations. Bull. Pol. Acad. Sci., Math. 41 (1993) 139–150. Zbl0796.60071MR1414761
  10. [10] Y.S. Mishura, Stochastic calculus for fractional Brownian motion and related processes. Springer (2007). Zbl1138.60006MR2378138
  11. [11] D. Nualart and A. Rascanu, Differential equations driven by fractional Brownian motion. Collect. Math.53 (2002) 55–81. Zbl1018.60057MR1893308
  12. [12] K. Yosida, Functional Analysis. Springer (1971). 

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