In this note, we prove an existence and uniqueness result of solution for stochastic differential delay equations with hereditary drift driven by a fractional Brownian motion with Hurst parameter H > 1/2. Then, we show that, when the delay goes to zero, the solutions to these equations converge, almost surely and in L p, to the solution for the equation without delay. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann–Stieltjes integral.
Convergence of delay differential equations driven by fractional Brownian motion
FERRANTE, MARCO;
2010
Abstract
In this note, we prove an existence and uniqueness result of solution for stochastic differential delay equations with hereditary drift driven by a fractional Brownian motion with Hurst parameter H > 1/2. Then, we show that, when the delay goes to zero, the solutions to these equations converge, almost surely and in L p, to the solution for the equation without delay. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann–Stieltjes integral.
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