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We consider the stochastic differential equations, ; dX t X t dt dB t t , ² ³ ~ ² ³ b ² ³ € / and ; where is fractional Brownian motion. We dX t X t dt dB t t B t ² ³ ~ ²!³ ² ³ b ² ³ € € ² ³ / / find solutions for these differential equations and show the existence of the integrals related to these solutions. We then show that is not a martingale. This(More)
Acknowledgements Dr. Edward J. Wegman, my dissertation co-advisor, deserves a special word of gratitude for his extraordinary support since I arrived at George Mason University. Throughout this dissertation and while taking his courses, Dr. Wegman very patiently spent numerous hours discussing my many questions. He went out of his way to be available(More)
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