A two-state neuronal model with alternating exponential excitation

DOI10.3934/mbe.2019171zbMath1497.92042OpenAlexW2937315529WikidataQ93200219 ScholiaQ93200219MaRDI QIDQ2160705

Nikita E. Ratanov

Publication date: 3 August 2022

Published in: Mathematical Biosciences and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/mbe.2019171

zbMATH Keywords

first passage timejump-telegraph processasymptotical behaviourneural activityfiring probability

Mathematics Subject Classification ID

Neural biology (92C20)

Related Items

Ornstein-Uhlenbeck processes of bounded variation ⋮ Special issue: Advances in stochastic processes and applications

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Time-Rescaling Theorem and Its Application to Neural Spike Train Data Analysis
• Telegraph processes and option pricing
• Occupation time distributions for the telegraph process
• On the first hitting time of a one-dimensional diffusion and a compound Poisson process
• Option pricing model based on a Markov-modulated diffusion with jumps
• Diffusion approximation of the neuronal model with synaptic reversal potentials
• Alternating oscillatory and stochastic dynamics in a model for a neuronal assembly
• The first passage time and estimation of the number of level-crossings for a telegraph process
• Asymptotic results for first-passage times of some exponential processes
• First crossing times of telegraph processes with jumps
• Piecewise deterministic processes in biological models
• A martingale analysis of first passage times of time-dependent Wiener diffusion models
• Sample path analysis and distributions of boundary crossing times
• Analysis of a stochastic neuronal model with excitatory inputs and state-dependent effects
• First Passage Times for Markov Additive Processes with Positive Jumps of Phase Type
• Introduction to Theoretical Neurobiology
• On a jump-telegraph process driven by an alternating fractional Poisson process
• On the Asymmetric Telegraph Processes
• Business Failures: Another Example of the Analysis of Failure Data
• An introduction to continuous-time stochastic processes. Theory, models, and applications to finance, biology, and medicine.
• Probabilistic analysis of the telegrapher's process with drift by means of relativistic transformations