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Continuous dependence of solutions of stochastic differential equations driven by standard and fractional Brownian motion on a parameter

Yu. S. Mishura, S. V. Posashkova, S. V. Posashkov
2011 Theory of Probability and Mathematical Statistics  
We consider a stochastic differential equation driven by both a Wiener process and a fractional Brownian motion. The coefficients of the equation are nonhomogeneous, and the initial condition is random. It is assumed that both the coefficients and the initial condition depend on a parameter. We establish conditions on the coefficients and the initial condition for the continuous dependence of a solution on the parameter.
doi:10.1090/s0094-9000-2012-00845-4 fatcat:jam57ogqqvhlrbbw4xfs7xww5q