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Publikováno v:
J. Math. Biol. (2018) 76: 679
Real time, or quantitative, PCR typically starts from a very low concentration of initial DNA strands. During iterations the numbers increase, first essentially by doubling, later predominantly in a linear way. Observation of the number of DNA molecu
Externí odkaz:
http://arxiv.org/abs/1609.07682
Autor:
Chigansky, Pavel, Kleptsyna, Marina
Publikováno v:
Stochastic Processes and Their Applications, Volume 128, Issue 6, June 2018, Pages 2007-2059
Many results in the theory of Gaussian processes rely on the eigenstructure of the covariance operator. However, eigenproblems are notoriously hard to solve explicitly and closed form solutions are known only in a limited number of cases. In this pap
Externí odkaz:
http://arxiv.org/abs/1601.05715
Autor:
Chigansky, Pavel, Kleptsyna, Marina
Publikováno v:
Teor. Veroyatnost. i Primenen., 63:3 (2018), 500-519
This paper addresses the problem of estimating drift parameter of the Ornstein - Uhlenbeck type process, driven by the sum of independent standard and fractional Brownian motions. The maximum likelihood estimator is shown to be consistent and asympto
Externí odkaz:
http://arxiv.org/abs/1507.04194
Publikováno v:
Annals of Probability 2016, Vol. 44, No. 4, 3032-3075
This paper presents a new approach to the analysis of mixed processes \[X_t=B_t+G_t,\qquad t\in[0,T],\] where $B_t$ is a Brownian motion and $G_t$ is an independent centered Gaussian process. We obtain a new canonical innovation representation of $X$
Externí odkaz:
http://arxiv.org/abs/1208.6253
Autor:
Chigansky, Pavel, Kutoyants, Yury
Publikováno v:
Mathematical Methods of Statistics, Vol 21, No. 2, 2012, pp 142-152
We consider the problem of threshold estimation for autoregressive time series with a "space switching" in the situation, when the regression is nonlinear and the innovations have a smooth, possibly non Gaussian, probability density. Assuming that th
Externí odkaz:
http://arxiv.org/abs/1110.0932
Autor:
Chigansky, Pavel, Klebaner, Fima C.
Publikováno v:
DCDS-Ser B., Vol. 17 Issue 5 pp. 1455-1471 (2012)
A standard convergence analysis of the simulation schemes for the hitting times of diffusions typically requires non-degeneracy of their coefficients on the boundary, which excludes the possibility of absorption. In this paper we consider the CEV dif
Externí odkaz:
http://arxiv.org/abs/1108.0307
Autor:
Chigansky, Pavel, van Handel, Ramon
Publikováno v:
Annals of Applied Probability 2010, Vol. 20, No. 6, 2318-2345
We develop necessary and sufficient conditions for uniqueness of the invariant measure of the filtering process associated to an ergodic hidden Markov model in a finite or countable state space. These results provide a complete solution to a problem
Externí odkaz:
http://arxiv.org/abs/0910.3603
Autor:
Chigansky, Pavel, Ritov, Yaacov
Publikováno v:
Bernoulli 2011, Vol. 17, No. 2, 609-627
This paper deals with convergence of the maximum a posterior probability path estimator in hidden Markov models. We show that when the state space of the hidden process is continuous, the optimal path may stabilize in a way which is essentially diffe
Externí odkaz:
http://arxiv.org/abs/0909.2139
Autor:
Chigansky, Pavel
Publikováno v:
Statistical Inference for Stochastic Processes, Volume 12, Number 2 / June, 2009, pp. 139-163
The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to I.Ibragimov and R.
Externí odkaz:
http://arxiv.org/abs/0707.0271