Weak solutions to stochastic differential equations driven by fractional Brownian motion

J. Šnupárková

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 4, page 879-907
  • ISSN: 0011-4642

Abstract

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Existence of a weak solution to the n -dimensional system of stochastic differential equations driven by a fractional Brownian motion with the Hurst parameter H ∈ ( 0 , 1 ) ∖ { 1 2 } is shown for a time-dependent but state-independent diffusion and a drift that may by split into a regular part and a singular one which, however, satisfies the hypotheses of the Girsanov Theorem. In particular, a stochastic nonlinear oscillator driven by a fractional noise is considered.

How to cite

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Šnupárková, J.. "Weak solutions to stochastic differential equations driven by fractional Brownian motion." Czechoslovak Mathematical Journal 59.4 (2009): 879-907. <http://eudml.org/doc/37965>.

@article{Šnupárková2009,
abstract = {Existence of a weak solution to the $n$-dimensional system of stochastic differential equations driven by a fractional Brownian motion with the Hurst parameter $H\in (0,1)\setminus \lbrace \frac\{1\}\{2\}\rbrace $ is shown for a time-dependent but state-independent diffusion and a drift that may by split into a regular part and a singular one which, however, satisfies the hypotheses of the Girsanov Theorem. In particular, a stochastic nonlinear oscillator driven by a fractional noise is considered.},
author = {Šnupárková, J.},
journal = {Czechoslovak Mathematical Journal},
keywords = {fractional Brownian motion; Girsanov theorem; weak solutions; fractional Brownian motion; Girsanov theorem; weak solution},
language = {eng},
number = {4},
pages = {879-907},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weak solutions to stochastic differential equations driven by fractional Brownian motion},
url = {http://eudml.org/doc/37965},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Šnupárková, J.
TI - Weak solutions to stochastic differential equations driven by fractional Brownian motion
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 4
SP - 879
EP - 907
AB - Existence of a weak solution to the $n$-dimensional system of stochastic differential equations driven by a fractional Brownian motion with the Hurst parameter $H\in (0,1)\setminus \lbrace \frac{1}{2}\rbrace $ is shown for a time-dependent but state-independent diffusion and a drift that may by split into a regular part and a singular one which, however, satisfies the hypotheses of the Girsanov Theorem. In particular, a stochastic nonlinear oscillator driven by a fractional noise is considered.
LA - eng
KW - fractional Brownian motion; Girsanov theorem; weak solutions; fractional Brownian motion; Girsanov theorem; weak solution
UR - http://eudml.org/doc/37965
ER -

References

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