Solutions of Backward Stochastic Differential Equations on Markov Chains

We consider backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We show that appropriate solutions exist for arbitrary terminal conditions, and are unique up to sets of measure zero. We do not require the generating functions to be monotonic, instead using only an appropriate Lipschitz continuity condition.Comment: To appear in Communications on Stochastic Analysis, August 200

Filters and smoothers for self-exciting Markov modulated counting processes

We consider a self-exciting counting process, the parameters of which depend on a hidden finite-state Markov chain. We derive the optimal filter and smoother for the hidden chain based on observation of the jump process. This filter is in closed form and is finite dimensional. We demonstrate the performance of this filter both with simulated data, and by analysing the `flash crash' of 6th May 2010 in this framework

An integrated neuro-mechanical model of C. elegans forward locomotion

One of the most tractable organisms for the study of nervous systems is the nematode Caenorhabditis elegans, whose locomotion in particular has been the subject of a number of models. In this paper we present a first integrated neuro-mechanical model of forward locomotion. We find that a previous neural model is robust to the addition of a body with mechanical properties, and that the integrated model produces oscillations with a more realistic frequency and waveform than the neural model alone. We conclude that the body and environment are likely to be important components of the worm’s locomotion subsystem

An integrated neuro-mechanical model of C. elegans forward locomotion

One of the most tractable organisms for the study of nervous systems is the nematode Caenorhabditis elegans, whose locomotion in particular has been the subject of a number of models. In this paper we present a first integrated neuro-mechanical model of forward locomotion. We find that a previous neural model is robust to the addition of a body with mechanical properties, and that the integrated model produces oscillations with a more realistic frequency and waveform than the neural model alone. We conclude that the body and environment are likely to be important components of the worm’s locomotion subsystem

Preferential duplication graphs

We consider a preferential duplication model for growing random graphs, extending previous models of duplication graphs by selecting the vertex to be duplicated with probability proportional to its degree. We show that a special case of this model can be analysed using the same stochastic approximation as for vertex-reinforced random walks, and show that 'trapping' behaviour can occur, such that the descendants of a particular group of initial vertices come to dominate the graph

Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions

Most previous contributions to BSDEs, and the related theories of nonlinear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Using solutions of BSDEs on spaces related to finite state, continuous time Markov chains, we develop a theory of nonlinear expectations in the spirit of [Dynamically consistent nonlinear evaluations and expectations (2005) Shandong Univ.]. We prove basic properties of these expectations and show their applications to dynamic risk measures on such spaces. In particular, we prove comparison theorems for scalar and vector valued solutions to BSDEs, and discuss arbitrage and risk measures in the scalar case.Comment: Published in at http://dx.doi.org/10.1214/09-AAP619 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Antenna design and development for the microwave subsystem experiments for the terminal configured vehicle project

The feasibility of classifying an airport terminal area for multipath effects, i.e., fadeout potentials or limits of video resolution, is examined. Established transmission links in terminal areas were modeled for landing approaches and overflight patterns. A computer program to obtain signal strength based on a described flight path was written. The application of this model to evaluate the signal transmission obtained in an actual flight equipped with additional signal strength monitoring equipment is described. The actual and computed received signal are compared, and the feasibility of the computer simulation for predicting signal amplitude fluctuation is evaluated

Large Magnetic Fields and Motions of OH Masers in W75 N

We report on a second epoch of VLBA observations of the 1665 and 1667 MHz OH masers in the massive star-forming region W75 N. We find evidence to confirm the existence of very strong (~40 mG) magnetic fields near source VLA 2. The masers near VLA 2 are dynamically distinct and include a very bright spot apparently moving at 50 km/s relative to those around VLA 1. This fast-moving spot may be an example of a rare class of OH masers seen in outflows in star-forming regions. Due to the variability of these masers and the rapidity of their motions, tracking these motions will require multiple observations over a significantly shorter time baseline than obtained here. Proper motions of the masers near VLA 1 are more suggestive of streaming along magnetized shocks rather than Keplerian rotation in a disk. The motions of the easternmost cluster of masers in W75 N (B) may be tracing slow expansion around an unseen exciting source.Comment: 7 pages including 4 figures (2 color) & 3 tables, to appear in Ap