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In this paper, we study a stationary control problem when the state process is a one di- mensional diffusion whose drift admits a unique, asymptotically stable equilibrium point
gave a general framework based on Yoshida’s theory of martingale expansion to prove the validity of such an asymptotic expansion around the Black-Scholes price for a general
The proof of Theorem 3 is based on Burkholder’s technique, which reduces the problem of proving a martingale inequality to finding a certain spe- cial function.. The description of
Incidentally, the class of stochastic processes we are considering covers simultaneously not only the Friedman urn, but also the walk with an asymptotically zero drift, first
For example in [3], the behaviour of a linear stochastic differential equation with an asymptotically vanishing delay term in the drift is shown to have different oscillatory
[1] study discretization schemes for stochastic differential equations with multivalued drift coefficients; Martinez and Talay [4] study discretization schemes for diffusion
For example, in [ 3 ] the uniqueness of the stochastic linear transport equation with Hölder continuous drift was proved, through new results about stochastic flows of class C 1,
Key words: Martingale, differential subordination, orthogonal martingales, moment inequality, stochastic integral, Brownian motion, best constants.. AMS 2000 Subject
