Stochastic differential equations with fractal noise
نویسنده
چکیده
Stochastic differential equations in R with random coefficients are considered where one continuous driving process admits a generalized quadratic variation process. The latter and the other driving processes are assumed to possess sample paths in the fractional Sobolev space W β 2 for some β > 1/2. The stochastic integrals are determined as anticipating forward integrals. A pathwise solution procedure is developed which combines the stochastic Itô calculus with fractional calculus via norm estimates of associated integral operators in W 2 for 0 < α < 1. Linear equations are considered as a special case. This approach leads to fast computer algorithms basing on Picard’s iteration method.
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