Statistical inference for piecewise-deterministic Markov processes

Statistical inference for piecewise-deterministic Markov processes /

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Bibliographic Details
Corporate Author: ProQuest (Firm)
Other Authors: Azais, Romain (Editor), Bouguet, Florian (Editor)
Format: Electronic eBook
Language:English
Published: London : ISTE, 2018.
Series:Mathematics and statistics series (ISTE)
Subjects:
Markov processes.
Online Access:Connect to this title online (unlimited simultaneous users allowed; 325 uses per year)

MARC

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245 0 0 |a Statistical inference for piecewise-deterministic Markov processes /  |c edited by Roman Azaïs, Florian Bouguet. 
264 1 |a London :  |b ISTE,  |c 2018. 
300 |a 1 online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a Mathematics and statistics 
504 |a Includes bibliographical references and index. 
505 0 0 |a Machine generated contents note:   |g ch. 1   |t Statistical Analysis for Structured Models on Trees /  |r Adelaide Olivier --   |g 1.1.  |t Introduction --   |g 1.1.1.  |t Motivation --   |g 1.1.2.  |t Genealogical versus temporal data --   |g 1.2.  |t Size-dependent division rate --   |g 1.2.1.  |t From partial differential equation to stochastic models --   |g 1.2.2.  |t Non-parametric estimation: the Markov tree approach --   |g 1.2.3.  |t Sketch of proof of Theorem 1.1 --   |g 1.3.  |t Estimating the age-dependent division rate --   |g 1.3.1.  |t Heuristics and convergence of empirical measures --   |g 1.3.2.  |t Estimation results --   |g 1.3.3.  |t Sketch of proof of Theorem 1.4 --   |g 1.4.  |t Bibliography --   |g ch. 2   |t Regularity of the Invariant Measure and Non-parametric Estimation of the Jump Rate /  |r Eva Locherbach --   |g 2.1.  |t Introduction --   |g 2.2.  |t Absolute continuity of the invariant measure --   |g 2.2.1.  |t dynamics --   |g 2.2.2.  |t associated Markov chain and its invariant measure --   |g 2.2.3.  |t Smoothness of the invariant density of a single particle --   |g 2.2.4.  |t Lebesgue density in dimension N --   |g 2.3.  |t Estimation of the spiking rate in systems of interacting neurons --   |g 2.3.1.  |t Harris recurrence --   |g 2.3.2.  |t Properties of the estimator --   |g 2.3.3.  |t Simulation results --   |g 2.4.  |t Bibliography --   |g ch. 3   |t Level Crossings and Absorption of an Insurance Model /  |r Alexandre Genadot --   |g 3.1.  |t insurance model --   |g 3.2.  |t Some results about the crossing and absorption features --   |g 3.2.1.  |t Transition density of the post-jump locations --   |g 3.2.2.  |t Absorption time and probability --   |g 3.2.3.  |t Kac-Rice formula --   |g 3.3.  |t Inference for the absorption features of the process --   |g 3.3.1.  |t Semi-parametric framework --   |g 3.3.2.  |t Estimators and convergence results --   |g 3.3.3.  |t Numerical illustration --   |g 3.4.  |t Inference for the average number of crossings --   |g 3.4.1.  |t Estimation procedures --   |g 3.4.2.  |t Numerical application --   |g 3.5.  |t Some additional proofs --   |g 3.5.1.  |t Technical lemmas --   |g 3.5.2.  |t Proof of Proposition 3.3 --   |g 3.5.3.  |t Proof of Corollary 3.2 --   |g 3.5.4.  |t Proof of Theorem 3.5 --   |g 3.5.5.  |t Proof of Theorem 3.6 --   |g 3.5.6.  |t Discussion on the condition (C2G) --   |g 3.6.  |t Bibliography --   |g ch. 4   |t Robust Estimation for Markov Chains with Applications to Piecewise-deterministic Markov Processes /  |r Charles Tillier --   |g 4.1.  |t Introduction --   |g 4.2.  |t (Pseudo)-regenerative Markov chains --   |g 4.2.1.  |t General Harris Markov chains and the splitting technique --   |g 4.2.2.  |t Regenerative blocks for dominated families --   |g 4.2.3.  |t Construction of regeneration blocks --   |g 4.3.  |t Robust functional parameter estimation for Markov chains --   |g 4.3.1.  |t influence function on the torus --   |g 4.3.2.  |t Example 1: sample means --   |g 4.3.3.  |t Example 2: M-estimators --   |g 4.3.4.  |t Example 3: quantiles --   |g 4.4.  |t Central limit theorem for functionals of Markov chains and robustness --   |g 4.5.  |t Markov view for estimators in PDMPs --   |g 4.5.1.  |t Example 1: Sparre Andersen model with barrier --   |g 4.5.2.  |t Example 2: kinetic dietary exposure model --   |g 4.6.  |t Robustness for risk PDMP models --   |g 4.6.1.  |t Stationary measure --   |g 4.6.2.  |t Ruin probability --   |g 4.6.3.  |t Extremal Index --   |g 4.6.4.  |t Expected shortfall --   |g 4.7.  |t Simulations --   |g 4.8.  |t Bibliography --   |g ch. 5   |t Numerical Method for Control of Piecewise-deterministic Markov Processes /  |r Francois Dufour --   |g 5.1.  |t Introduction --   |g 5.2.  |t Simulation of piecewise-deterministic Markov processes --   |g 5.3.  |t Optimal stopping --   |g 5.3.1.  |t Assumptions and notations --   |g 5.3.2.  |t Dynamic programming --   |g 5.3.3.  |t Quantized approximation --   |g 5.4.  |t Exit time --   |g 5.4.1.  |t Problem setting and assumptions --   |g 5.4.2.  |t Recursive formulation --   |g 5.4.3.  |t Numerical approximation --   |g 5.5.  |t Numerical example --   |g 5.5.1.  |t Piecewise-deterministic Markov model --   |g 5.5.2.  |t Deterministic time to reach the boundary --   |g 5.5.3.  |t Quantization --   |g 5.5.4.  |t Optimal stopping --   |g 5.5.5.  |t Exit time --   |g 5.6.  |t Conclusion --   |g 5.7.  |t Bibliography --   |g ch. 6   |t Rupture Detection in Fatigue Crack Propagation /  |r Florine Greciet --   |g 6.1.  |t Phenomenon of crack propagation --   |g 6.1.1.  |t Virkler's data --   |g 6.2.  |t Modeling crack propagation --   |g 6.2.1.  |t Deterministic models --   |g 6.2.2.  |t Sources of uncertainties --   |g 6.2.3.  |t Stochastic models --   |g 6.3.  |t PDMP models of propagation --   |g 6.3.1.  |t Relevance of PDMP models --   |g 6.3.2.  |t Multiplicative model --   |g 6.3.3.  |t One-jump models --   |g 6.4.  |t Rupture detection --   |g 6.4.1.  |t Length at versus time t --   |g 6.4.2.  |t Growth rate dat / dt versus ΔKt in log scale --   |g 6.5.  |t Conclusion and perspectives --   |g 6.6.  |t Bibliography --   |g ch. 7   |t Piecewise-deterministic Markov Processes for Spatio-temporal Population Dynamics /  |r Samuel Soubeyrand --   |g 7.1.  |t Introduction --   |g 7.1.1.  |t Models of population dynamics --   |g 7.1.2.  |t Spatio-temporal PDMP for population dynamics --   |g 7.1.3.  |t Chapter contents --   |g 7.2.  |t Stratified dispersal models --   |g 7.2.1.  |t Reaction-diffusion equations for modeling short-distance dispersal --   |g 7.2.2.  |t Stratified diffusion --   |g 7.2.3.  |t Coalescing colony model with Allee effect --   |g 7.2.4.  |t PDMP based on reaction-diffusion for modeling invasions with multiple introductions --   |g 7.3.  |t Metapopulation epidemic model --   |g 7.3.1.  |t Spatially realistic Levins model --   |g 7.3.2.  |t colonization PDMP --   |g 7.3.3.  |t Bayesian inference approach --   |g 7.3.4.  |t Markov chain Monte Carlo algorithm --   |g 7.3.5.  |t Examples of results --   |g 7.4.  |t Stochastic approaches for modeling spatial trajectories --   |g 7.4.1.  |t Conditioning a Brownian motion by punctual observations --   |g 7.4.2.  |t Movements with jumps --   |g 7.4.3.  |t Doleans-Dade exponential semi-martingales --   |g 7.4.4.  |t Statistical issues --   |g 7.5.  |t Conclusion --   |g 7.6.  |t Bibliography. 
533 |a Electronic reproduction.  |b Ann Arbor, MI  |n Available via World Wide Web. 
588 |a Online resource; title from PDF title page (EBSCO, viewed August 6, 2018). 
650 0 |a Markov processes. 
700 1 |a Azais, Romain,  |e editor. 
700 1 |a Bouguet, Florian,  |e editor. 
710 2 |a ProQuest (Firm) 
830 0 |a Mathematics and statistics series (ISTE) 
856 4 0 |u https://ebookcentral.proquest.com/lib/santaclara/detail.action?docID=5484224  |z Connect to this title online (unlimited simultaneous users allowed; 325 uses per year)  |t 0 
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919 |a .ulebk  |b 2017-02-14 
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