Stochastic Calculus for Fractional Brownian Motion and Applications
Publication year: 2008
ISBN: 978-1-84628-797-8
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Fractional Brownian motion (fBm) has been widely used to model a number of phenomena in diverse fields from biology to finance. This huge range of potential applications makes fBm an interesting object of study. fBm represents a natural one-parameter extension of classical Brownian motion therefore it is natural to ask if a stochastic calculus for fBm can be developed. This is not obvious, since fBm is neither a semimartingale (except when H = ½), nor a Markov process so the classical mathematical machineries for stochastic calculus are not available in the fBm case.
Subject: Mathematics and Statistics, Brownian motion, Markov, Markov process, Martingale, Potential, Probability theory, Semimartingale, Stochastic calculus, calculus, equation, fractional Brownian motion, local time, mathematics, model, partial differential equation
