Standard Brownian Motion Model Research Articles

The pricing formulas of compound option based on the sub-fractional Brownian motion model

Based on the underlying asset driven by a sub-fractional Brownian motion, the formulas of pricing call option on a call option and other three kinds of compound options are derived by risk neutral valuation method. They are similar to the results based on the standard Brownian motion model and the fractional Brownian motion model.

Unified model for the study of diffusion localization and dissipation

A model that generalizes the study of quantum Brownian motion (BM) is constructed. We consider disordered environment that may be either static (quenched), noisy or dynamical. The Zwanzig-Caldeira-Leggett BM model formally constitutes a special case where the disorder autocorrelation length is taken to be infinite. Alternatively, a localization problem is obtained if the noise autocorrelation time is taken to be infinite. Also the general case of weak nonlinear coupling to a thermal, possibly chaotic bath is handled by the same formalism. A general, Feynman-Vernon type path-integral expression for the propagator is introduced. A Wigner transformed version of this expression is utilized in order to facilitate comparison with the classical limit. It is demonstrated that nonstochastic genuine quantal manifestations are associated with the model. It is clarified that such effects are absent in the standard BM model, either the disorder or the chaotic nature of the bath are essential. Quantal correction to the classical diffusive behavior is found even in the limit of high temperatures. The suppression of interference due to dephasing is discussed, leading to the observation that due to the disorder the decay of coherence is exponential in time, and no longer depends on geometrical considerations. Fascinating non-Markovian effects due to time-correlated (colored) noise are explored. For this, a strategy is developed in order to handle the integration over paths. This strategy is extended in order to demonstrate how localization comes out from the path-integral expression.

Phase-noise-induced performance limits for DPSK modulation with and without frequency feedback

The effect of phase noise on the performance of differential phase shift keying (DPSK) is analyzed for four different receiver structures. The phase noise model used is more general than the standard Brownian motion model. It allows the observation of the effect of frequency feedback stabilization on system performance. The asymptotic performance in the limit as the signal-to-noise ratio tends to infinity is considered. The results show that feedback stabilization results in a considerable performance improvement. For example, in a narrowband receiver this scheme results in an effective linewidth reduction by a factor of 12.5 when the feedback bandwidth is 0.8 times the bit rate, and by a factor of 42 when the feedback bandwidth is 1.6 times the bit rate. Therefore, frequency feedback reduces the minimum required data rate for a given laser linewidth, or increases the maximum linewidth allowed for a given data rate. The performance of the narrowband receiver in the presence of both additive and phase noises is determined and a dramatic improvement with feedback is shown.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>