Existence and uniqueness of solution
Teoriâ slučajnyh processov, Tome 13 (2007) no. 2, pp. 152-165.

Voir la notice de l'article provenant de la source Math-Net.Ru

The existence and uniqueness of solution of stochastic differential equation driven by standard Brownian motion and fractional Brownian motion with Hurst parameter $H\in(3/4, 1)$ is established.
Keywords: Stochastic differential equation, fractional Brownian motion.
@article{THSP_2007_13_2_a0,
     author = {Yulia Mishura and Sergiy Posashkov},
     title = {Existence and uniqueness of solution},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {152--165},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2007_13_2_a0/}
}
TY  - JOUR
AU  - Yulia Mishura
AU  - Sergiy Posashkov
TI  - Existence and uniqueness of solution
JO  - Teoriâ slučajnyh processov
PY  - 2007
SP  - 152
EP  - 165
VL  - 13
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2007_13_2_a0/
LA  - en
ID  - THSP_2007_13_2_a0
ER  - 
%0 Journal Article
%A Yulia Mishura
%A Sergiy Posashkov
%T Existence and uniqueness of solution
%J Teoriâ slučajnyh processov
%D 2007
%P 152-165
%V 13
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2007_13_2_a0/
%G en
%F THSP_2007_13_2_a0
Yulia Mishura; Sergiy Posashkov. Existence and uniqueness of solution. Teoriâ slučajnyh processov, Tome 13 (2007) no. 2, pp. 152-165. http://geodesic.mathdoc.fr/item/THSP_2007_13_2_a0/

[1] D. Nualart, Răşcanu, “Differential equations driven by fractional Brownian motion”, Collect. Math., 53 (2000), 55–81

[2] P. Cheridito Regularizing fractional Brownian motion with a view towards stock price modeling, PhD thesis, Zurich, 2001

[3] Yu. Mishura, S. Posashkov, “Existence and uniqueness of solution of stochastic differential equation driven by fractional Brownian motion with stabilizing term”, Theory Prob. Math. Stat., 76 (2007)

[4] M. Zähle, “On the link between fractional and stochastic calculcus”, Stochastic Dynamics, eds. Grauel, H., Gundlach, M., Springer, 1999, 305–325

[5] M. Zähle, “Integration with respect to fractal functions and stochastic calculus. I”, Probab. Theory Rel. Fields, 111 (1998), 333–374

[6] M. Zähle Integraton with respect to fractal functions and stochastic calculus. II, Math. Nachr., 225 (2001), 145–183

[7] Yu. Krvavych, Yu. Mishura, “Exponential formula and Girsanov theorem for mixed semilinear stochastic differential equatios”, Mathematical Finance (Trends in Mathematics), Basel, Birkhäuser, 2001, 230–239

[8] M. Hitsuda, “Representation of Gaussian processes equivalent to Wiener process”, Osaka Journal of Mathematics, 5 (1968), 299–312