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We study the existence, uniqueness and approximation of solutions of general stochastic differential equations (SDEs) with two time-dependent reflecting barriers driven by semimartingales and processes with bounded p -variation, p ∈ [ 1 , 2). We do not assume that the barriers have to be completely separated. Applications to currency option pricing in financial models with fractional Brownian motion and standard Brownian motion are given. [ABSTRACT FROM AUTHOR]

It is shown that every adapted Brownian bridge on a geodesically complete connected Riemannian manifold is a semimartingale including its terminal time, without any further assumptions on the geometry. In particular, it follows that every such process can be horizontally lifted to a smooth principal fiber bundle with connection, including its terminal time. The proof is based on a localized Hamilton-type gradient estimate. [ABSTRACT FROM AUTHOR]

We give an account of the characteristics that result from reflecting a drifting local martingale (i.e. the sum of a local martingale and a multiple of its quadratic variation process) in 0 and b > 0. We present conditions which guarantee the existence of finite moments of what is required to keep the reflected process within its boundaries. Also, we derive an associated law of large numbers and a central limit theorem which apply when the input is continuous. Similar results for integrals of the paths of the reflected process are also presented. These results are in close agreement to what has previously been shown for Brownian motion. [ABSTRACT FROM AUTHOR]

We prove that a sequence of diffusion processes in ℝ n that are Brownian motions with drift unboundedly increasing in modulus and directed to a manifold converges in distribution to the Brownian motion on the manifold. [ABSTRACT FROM AUTHOR]