Viability for differential equations driven by fractional Brownian motion

Journal of Differential Equations

Volumn 247, Issue 5, 2009, Pages 1505-1528

  Ciotir, Ioana ^a   Rǎşcanu, Aurel ^a,b  

^a ALEXANDRU IOAN CUZA UNIVERSITY OF IASI   (Romania)

^b ACADEMY OF ROMANIAN SCIENTISTS   (Romania)

Author keywords

Fractional Brownian motion; Stochastic differential equations; Viability

Indexed keywords

EID: 67650163462     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2009.06.002     Document Type: Article

References (18)

1. Alòs E., Mazet O., and Nualart D. Stochastic calculus with respect to Gaussian processes. Ann. Probab. 29 (2001) 766-801
2. Aubin J.-P. Viability Theory (1992), Birkhäuser
3. Aubin J.-P., and Da Prato G. Stochastic viability and invariance. Ann. Sc. Norm. Super. Pisa Cl. Sci. 27 (1990) 595-694
4. Aubin J.-P., and Da Prato G. The viability theorem for stochastic differential inclusions. Stoch. Anal. Appl. 16 1 (1998) 1-15
5. Buckdahn R., Quincampoix M., Rainer C., and Rascanu A. Viability of moving sets for stochastic differential equation. Adv. Differential Equations 7 9 (2002) 1045-1072
6. Carmona P., and Coutin L. Stochastic integration with respect to fractional Brownian motion. Ann. Inst. H. Poincaré Probab. Statist. 39 (2003) 27-68
7. Decreusefond L., and Üstünel A.S. Stochastic analysis of the fractional Brownian motion. Potential Anal. 10 (1998) 177-214
8. Duncan T.E., Hu Y., and Pasik-Duncan B. Stochastic calculus for fractional Brownian motion I, Theory. SIAM J. Control Optim. 38 2 (2000) 582-612
9. Gautier S., and Thibault L. Viability for constrained stochastic differential equations. Differential Integral Equations 6 (1993) 1394-1414
10. Hu Y., and Oksendal B. Fractional white noise calculus and applications to finance. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 6 (2003) 1-32
11. Mandelbrot B.B., and Van Ness J.W. Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10 (1968) 422-437
12. Michta M. A note on viability under distribution constraints. Discuss. Math., Algebra Stoch. Methods 18 2 (1998) 215-225
13. Milian A. A note on stochastic invariance for Ito equations. Bull. Pol. Acad. Sci. Math. 41 2 (1993) 139-150
14. Motyl J. Viability of set-valued Ito equation. Bull. Pol. Acad. Sci. Math. 47 1 (1999) 91-103
15. Nualart D., and Rascanu A. Differential equations driven by fractional Brownian motion. Collect. Math. 53 (2002) 55-81
16. Young L.C. An inequality of the Hölder type connected with Stieltjes integration. Acta Math. 67 (1936) 251-282
17. Zähle M. Integration with respect to fractal functions and stochastic calculus. I. Probab. Theory Related Fields 111 (1998) 333-374
18. Zähle M. On the link between fractional and stochastic calculus. In: Crauel H., and Gundlach M. (Eds). Stochastic Dynamics. Bremen 1997 (1999), Springer 305-325