# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Stochastic differential equations driven by a Wiener process and fractional Brownian motion: convergence in Besov space with respect to a parameter. (English) Zbl 1228.60067
Summary: A stochastic differential equation involving both a Wiener process and fractional Brownian motion, with nonhomogeneous coefficients and random initial condition, is considered. The coefficients and initial condition depend on a parameter. The assumptions on the coefficients and the initial condition supplying continuous dependence of the solution on a parameter, with respect to the Besov space norm, are established.

##### MSC:
 60H10 Stochastic ordinary differential equations 34A08 Fractional differential equations
Full Text:
##### References:
 [1] Mishura, Yu.S.: Stochastic calculus for fractional Brownian motion and related processes, Lecture notes in mathematics (2008) [2] Yu.S. Mishura, G.M. Shevchenko, Stochastic differential equation involving Wiener process and fractional Brownian motion with Hurst index H>1/2, Comm. Statist. Theory Methods (in press). · Zbl 1315.60071 [3] Nualart, D.; Răşcanu, A.: Differential equation driven by fractional Brownian motion, Collect. math. 53, No. 1, 55-81 (2002) · Zbl 1018.60057 [4] Zähle, M.: On the link between fractional and stochastic calculus, Stochastic dynamics, Bremen, 305-325 (1997) · Zbl 0947.60060 [5] Zähle, M.: Integration with respect to fractal functions and stochastic calculus. I, Probab. theory related fields 111, 333-374 (1988) · Zbl 0918.60037 · doi:10.1007/s004400050171 [6] Samko, S. G.; Kilbas, A. A.; Marichev, O. I.: Fractional integrals and derivatives, (1993) · Zbl 0818.26003 [7] Fernique, X. M.: Regularitè des trajectories de fonctions alèatories gaussiennes, Lect. notes math. (1974)