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- Peter Baxendale
- 2003

We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and Tweedie, and from estimates using coupling, although we start from essentially the same assumptions of a drift condition… (More)

- Peter Baxendale, Pavel Chigansky, Robert Sh. Liptser
- SIAM J. Control and Optimization
- 2004

The stability problem of the Wonham filter with respect to initial conditions is addressed. The case of ergodic signals is revisited in view of a gap in the classic work of H. Kunita (1971). We give new bounds for the exponential stability rates, which do not depend on the observations. In the nonergodic case, the stability is implied by identifiability… (More)

- Peter Baxendale, Priscilla E. Greenwood
- Journal of mathematical biology
- 2011

Simulations of models of epidemics, biochemical systems, and other bio-systems show that when deterministic models yield damped oscillations, stochastic counterparts show sustained oscillations at an amplitude well above the expected noise level. A characterization of damped oscillations in terms of the local linear structure of the associated dynamics is… (More)

- Peter Baxendale
- 2003

Consider the stochastic Duffing-van der Pol equation ẍ = −ω2x− Ax −Bx2ẋ + εβẋ + εσxẆt with A ≥ 0 and B > 0. If β/2 + σ/8ω > 0 then for small enough ε > 0 the system (x, ẋ) is positive recurrent in R \ {0}. Let λ̃ε denote the top Lyapunov exponent for the linearization of this equation along trajectories. The main result asserts that λ̃ε ∼ ελ̃ as ε → 0 where… (More)

- Peter Baxendale
- 2002

Let λ denote the almost sure Lyapunov exponent obtained by linearizing the stochastic Duffing-van der Pol oscillator ẍ = −ωx + βẋ−Ax −Bxẋ + σxẆt at the origin x = ẋ = 0 in phase space. If λ > 0 then the process {(xt, ẋt) : t ≥ 0} is positive recurrent on R \ {(0, 0)} with stationary probability measure μ, say. For λ > 0 let λ̃ denote the almost sure… (More)

An Ant-Based Routing System has been constructed and it has been shown to find optimum routing strategies under static conditions. With the introduction of dynamic traffic situations onto the network, the ants do not always display optimum behaviour. It has been shown that parameters cannot be set to a single value to satisfy both steady state and… (More)

Integrate and fire oscillators are widely used to model the generation of action potentials in neurons. In this paper, we discuss small noise asymptotic results for a class of stochastic integrate and fire oscillators (SIFs) in which the buildup of membrane potential in the neuron is governed by a Gaussian diffusion process. To analyze this model, we study… (More)

Future users of large data banks must be protected from having to know how the data is organized in the machine (the internal representation). A prompting service which supplies such information is not a satisfactory solution. Activities of users at terminals and most application programs should remain unaffected when the internal representation of data is… (More)

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