Causal Point Process Transformations

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Table of contents

Summary
Acknowledgments
I Introduction
1 General Introduction
1.1 Synopsis
1.2 Framework Description
1.3 Applications
1.4 State of the Art and Main Contributions
1.5 Thesis Outline
2 Analytical Tools
2.1 Poisson Point Processes
2.1.1 Poisson Point Processes in the Real Line
2.1.2 PPP Transformations
2.1.3 Membrane Equation as PPP transformation
2.1.4 Statistics of PPP transformations
2.2 General Solution
2.2.1 Additive Noise
2.2.2 Multiplicative Noise
2.2.3 General Case
2.3 Asymptotic and Stationary Limits
2.4 Random Dirac Delta Sums
2.5 Compound PPP Transformations
2.6 Central Moments Expansion
Appendix A
A.1 Sampling Procedure
A.2 Numerical Integration of Membrane Equation
A.3 Cumulants of Integral PPP Transformations
A.4 Two Independent Conductance Inputs
A.5 General Case
A.6 Random Dirac Delta Sums
A.7 Shot Noise Cumulants
A.8 Expectation of Random Product
II Research Articles
3 Nonstationary filtered shot-noise processes and applications to neuronal membranes
4 The impact of synaptic conductance inhomogeneities on membrane potential statistics
5 How causal correlations between synaptic inputs affect membrane potential fluctuations
6 Estimating stochastic process memory in neuronal membranes
III Discussion
7 General Discussion