29 citations · 64 across the 13 of their papers we have counts for
8 papers · 1 filter
Almost-Sure Stability of the Single Mode Solution of a Noisy Nonlinear Autoparametric System
Peter H. Baxendale, N. Sri Namachchivaya
For a pendulum suspended below a vibrating block with white noise forcing, the solution in which the pendulum remains vertical is called the single mode solution. When this solutio…
Quantitative Convergence of the Filter Solution for Multiple Timescale Nonlinear Systems with Coarse-Grain Correlated Noise
Ryne Beeson, N. Sri Namachchivaya, Nicolas Perkowski
In this paper we prove a rate of convergence for the continuous time filtering solution of a multiple timescale correlated nonlinear system to a lower dimensional filtering equatio…
Approximation of the Filter Equation for Multiple Timescale, Correlated, Nonlinear Systems
Ryne Beeson, N. Sri Namachchivaya, Nicolas Perkowski
This paper considers the approximation of the continuous time filtering equation for the case of a multiple timescale (slow-intermediate, and fast scales) that may have correlation…
Exponentially-ergodic Markovian noise perturbations of delay differential equations at Hopf bifurcation
Nishanth Lingala, Navaratnam Sri Namachchivaya, Volker Wihstutz
We consider noise perturbations of delay differential equations (DDE) experiencing Hopf bifurcation. The noise is assumed to be exponentially ergodic, i.e. transition density conve…
Random Perturbations of a Periodically Driven Nonlinear Oscillator: Escape from a resonance zone
Nishanth Lingala, Navaratnam Sri Namachchivaya, Ilya Pavlyukevich
The phase space for a periodically driven nonlinear oscillator consists of many resonance zones. Let the strength of periodic excitation and the strength of the damping be indexed…
Perturbations of linear delay differential equations at the verge of instability
Nishanth Lingala, N. Sri Namachchivaya
The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge…
Nonlinear and additive white noise perturbations of linear delay differential equations at the verge of instability: an averaging approach
Nishanth Lingala, N. Sri Namachchivaya
The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. We deal with linear DDEs that are on the verge of inst…
Dimensional reduction in nonlinear filtering: A homogenization approach
Peter Imkeller, N. Sri Namachchivaya, Nicolas Perkowski +1
We propose a homogenized filter for multiscale signals, which allows us to reduce the dimension of the system. We prove that the nonlinear filter converges to our homogenized filte…