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Abstract
Exact discretization formulae are established for a first-order stochastic differential equation driven by a fractional noise of either long memory or antipersistent type. We assume that the underlying process is sampled at non-unit equispaced observational intervals. Using fractional algebra techniques the exact discretization formulae are derived in terms of confluent hypergeometric and incomplete gamma functions which admit infinite order series expansions.
Keywords: stochastic differential equations; fractional noise; exact discretization formulae; special functions
Published Online: 2012-11-14
©2012 Walter de Gruyter GmbH & Co. KG, Berlin/Boston