Probabilistic state estimation for labeled continuous time Markov models with applications to attack detection

The objective of this thesis is to provide a simulations-free approximation to the price of multivariate derivatives and for the calculation of risk measures like Value at Risk (VaR). The first chapters are dedicated to the pricing of multivariate derivatives. In particular we focus on multivariate derivatives under switching regime Markov models. We consider the cases of two and three states of the switching regime Markov model, and derive analytic expressions for the first and second order moments of the occupation times of the continuous-time Markov process. Then we use these expressions to provide approximations for the derivative prices based on Taylor expansions. We compare our closed form approximations with Monte Carlo simulations. In the last chapter we also provide a simulations-free approximation for the VaR under a switching regime model with two states. We compare these VaR estimations with those obtained using Monte Carlo.

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A Simple And Novel Algorithm For State Estimation Of Continuous Time Linear Stochastic Dynamic Systems Excited By Random Inputs

International Journal of Innovative Technology and Exploring Engineering - Special Issue ◽

10.35940/ijitee.j9767.0881019 ◽

2019 ◽

Vol 8 (10) ◽

pp. 3559-3563

Keyword(s):

Kalman Filter ◽

State Estimation ◽

Continuous Time ◽

Stochastic Dynamic ◽

Time Dynamic ◽

Time Dynamics ◽

Hardware Realization ◽

Aerial Vehicle ◽

Non Linear System ◽

Stochastic Dynamic Systems

The major goal of this paper is to explore the effective state estimation algorithm for continuous time dynamic system under the lossy environment without increasing the complexity of hardware realization. Though the existing methods of state estimation of continuous time system provides effective estimation with data loss, the real time hardware realization is difficult due to the complexity and multiple processing. Kalman Filter and Particle Filer are fundamental algorithms for state estimation of any linear and non-linear system respectively, but both have its limitation. The approach adopted here, detect the expected state value and covariance, existed by random input at each stage and filtered the noisy measurement and replace it with predicted modified value for the effective state estimation. To demonstrate the performance of the results, the continuous time dynamics of position of the Aerial Vehicle is used with proposed algorithm under the lossy measurements scenario and compared with standard Kalman filter and smoothed filter. The results show that the proposed method can effectively estimate the position of Aerial Vehicle compared to standard Kalman and smoothed filter under the non-reliable sensor measurements with less hardware realization complexity.

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Clustering of Bursts of Openings in Markov and Semi-Markov Models of Single Channel Gating

Advances in Applied Probability ◽

10.1017/s0001867800027804 ◽

1997 ◽

Vol 29 (01) ◽

pp. 92-113 ◽

Cited By ~ 2

Author(s):

Frank Ball ◽

Sue Davies

Keyword(s):

Markov Chain ◽

Ion Channel ◽

State Space ◽

Continuous Time ◽

Markov Models ◽

Numerical Study ◽

Channel Gating ◽

Markov Renewal Process ◽

Time Interval ◽

Continuous Time Markov Chain

The gating mechanism of a single ion channel is usually modelled by a continuous-time Markov chain with a finite state space. The state space is partitioned into two classes, termed ‘open’ and ‘closed’, and it is possible to observe only which class the process is in. In many experiments channel openings occur in bursts. This can be modelled by partitioning the closed states further into ‘short-lived’ and ‘long-lived’ closed states, and defining a burst of openings to be a succession of open sojourns separated by closed sojourns that are entirely within the short-lived closed states. There is also evidence that bursts of openings are themselves grouped together into clusters. This clustering of bursts can be described by the ratio of the variance Var (N(t)) to the mean[N(t)] of the number of bursts of openings commencing in (0, t]. In this paper two methods of determining Var (N(t))/[N(t)] and limt→∝Var (N(t))/[N(t)] are developed, the first via an embedded Markov renewal process and the second via an augmented continuous-time Markov chain. The theory is illustrated by a numerical study of a molecular stochastic model of the nicotinic acetylcholine receptor. Extensions to semi-Markov models of ion channel gating and the incorporation of time interval omission are briefly discussed.

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