Publications (26)
Populations with interaction and environmental dependence: from few, (almost) independent, members into deterministic evolution of high densities
P. Chigansky, P. Jagers, F. C. Klebaner
Many populations, e.g. of cells, bacteria, viruses, or replicating DNA molecules, start small, from a few individuals, and grow large into a noticeable fraction of the environmenta…
Distribution of the Brownian motion on its way to hitting zero
P. Chigansky, F. C. Klebaner
For the one-dimensional Brownian motion , started at , and the first hitting time , we find the probability density of for…
An approximation of populations on a habitat with large carrying capacity
N. Bauman, P. Chigansky, F. Klebaner
We consider stochastic dynamics of a population which starts from a small colony on a habitat with large but limited carrying capacity. A common heuristics suggests that such popul…
On exponential stability of Wonham filter
P. Chigansky, R. Liptser
We give elementary proof of a stability result concerning an exponential asymptotic () for filtering estimates generated by wrongly initialized Wonham filter. This proo…
On the establishment of a mutant
J. Baker, P. Chigansky, P. Jagers +1
How long does it take for an initially advantageous mutant to establish itself in a resident population, and what does the population composition look like then? We approach these…
On a role of predictor in the filtering stability
P. Chigansky, R. Liptser
When is a nonlinear filter stable with respect to its initial condition? In spite of the recent progress, this question still lacks a complete answer in general. Currently availabl…
Stability of the nonlinear filter for slowly switching Markov chains
P. Chigansky
Exponential stability of the nonlinear filtering equation is revisited, when the signal is a finite state Markov chain. An asymptotic upper bound for the filtering error due to inc…
Estimation in threshold autoregressive models with correlated innovations
P. Chigansky, Y. Kutoyants
Large sample statistical analysis of threshold autoregressive (TAR) models is usually based on the assumption that the underlying driving noise is uncorrelated. In this paper, we c…
Asymptotic analysis of the finite predictor for fractional Gaussian noise
P. Chigansky, M. Kleptsyna
This paper proposes a new approach to the asymptotic analysis of the finite predictor for stationary sequences. Our method yields the exact asymptotics of both the relative predict…
On the emergence of random initial conditions in fluid limits
A. D. Barbour, P. Chigansky, F. C. Klebaner
The paper presents a phenomenon occurring in population processes that start near zero and have large carrying capacity. By the classical result of Kurtz~(1970), such processes, no…
Sharp asymptotics in a fractional Sturm-Liouville problem
P. Chigansky, M. Kleptsyna
The current research of fractional Sturm-Liouville boundary value problems focuses on the qualitative theory and numerical methods, and much progress has been recently achieved in…
Mixed fractional Brownian motion: a spectral take
P. Chigansky, M. Kleptsyna, D. Marushkevych
This paper provides yet another look at the mixed fractional Brownian motion (fBm), this time, from the spectral perspective. We derive an approximation for the eigenvalues of its…
Exact spectral asymptotics of fractional processes
P. Chigansky, M. Kleptsyna, D. Marushkevych
Eigenproblems frequently arise in theory and applications of stochastic processes, but only a few have explicit solutions. Those which do, are usually solved by reduction to the ge…
Linear filtering with fractional noises: large time and small noise asymptotics
D. Afterman, P. Chigansky, M. Kleptsyna +1
The classical state-space approach to optimal estimation of stochastic processes is efficient when the driving noises are generated by martingales. In particular, the weight functi…
On filtering of Markov chains in strong noise
P. Chigansky
The filtering problem for finite state Markov chains is revisited, when the intensity of the observation noise increases. We give a description of conditional measure concentration…
Persistence of Small Noise and Random initial conditions
J. Baker, P. Chigansky, K. Hamza +1
The effect of small noise in a smooth dynamical system is negligible on any finite time interval. Here we study situations when it persists on intervals increasing to infinity. Suc…
Estimation of the Hurst parameter from continuous noisy data
P. Chigansky, M. Kleptsyna
This paper addresses the problem of estimating the Hurst exponent of the fractional Brownian motion from continuous time noisy sample. Consistent estimation in the setup under cons…
The Freidlin-Wentzell LDP with rapidly growing coefficients
P. Chigansky, R. Liptser
The Large Deviations Principle (LDP) is verified for a homogeneous diffusion process with respect to a Brownian motion , $$ X^\eps_t=x_0+\int_0^tb(X^\eps_s)ds+ \eps\int_0^tÏ(…
Asymptotic accuracy in estimation of a fractional signal in a small white noise
M. Kleptsyna, D. Marushkevych, P. Chigansky
This paper revisits the problem of estimating the fractional Ornstein - Uhlenbeck process observed in a linear channel with white noise of small intensity. We drive the exact asymp…
Compound Poisson approximation for triangular arrays with application to threshold estimation
P. Chigansky, F. C. Klebaner
We prove weak convergence of triangular arrays to the compound Poisson limit using Tikhomirov's method. The result is applied to statistical estimation of the threshold parameter i…
Large deviations for a scalar diffusion in random environment
P. Chigansky, R. Liptser
Let , be an ergodic stationary Markov chain, taking a finite number of values , and , where is a bounded and measurable fun…
Multitype PCR branching processes
P. Chigansky, F. Klebaner, M. Mrksa +1
To model amplification Polymerase Chain Reaction (PCR) techniques targeting DNA sequences of several types, we introduce a multitype PCR branching process as a generalized version…
On the eigenproblem for Gaussian bridges
P. Chigansky, M. Kleptsyna, D. Marushkevych
Spectral decomposition of the covariance operator is one of the main building blocks in the theory and applications of Gaussian processes. Unfortunately it is notoriously hard to d…
An ergodic theorem for filtering with applications to stability
P. Chigansky
Ergodic properties of the signal-filtering pair are studied for continuous time finite Markov chains, observed in white noise. The obtained law of large numbers is applied to the s…
Asymptotic stability of the Wonham filter for ergodic and nonergodic signals
P. Baxendale, P. Chigansky, R. Liptser
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 (…
Asymptotic analysis in problems with fractional processes
P. Chigansky, M. Kleptsyna
Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, v…