Stochastic Viability and Comparison Theorems for Mixed Stochastic Differential Equations
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For a mixed stochastic differential equation containing both Wiener process and a Hölder continuous process with exponent γ > 1/2, we prove a stochastic viability theorem. As a consequence, we get a result about positivity of solution and a pathwise comparison theorem. An application to option price estimation is given.
KeywordsMixed stochastic differential equation Pathwise integral Stochastic viability Comparison theorem Long-range dependence fractional Brownian motion Stochastic differential equation with random drift
AMS 2000 Subject Classifications60G22 60G15 60H10 26A33
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- Cheridito P (2001) Regularizing fractional Brownian motion with a view towards stock price modelling. PhD thesis, Swiss Federal Institute Of Technology, ZurichGoogle Scholar
- Ikeda N, Watanabe S (1989) Stochastic differential equations and diffusion processes. In: North-Holland Mathematical Library, vol 24, 2nd edn. North-Holland, AmsterdamGoogle Scholar
- Ioffe M (2010) Probability distribution of Cox–Ingersoll–Ross process. Working paper, Egar Technology, New YorkGoogle Scholar
- Samko SG, Kilbas AA, Marichev OI (1993) Fractional integrals and derivatives. Theory and applications. Gordon and Breach Science, New YorkGoogle Scholar