Probability law and flow function of Brownian motion driven by a generalized telegraph process

DOI10.1007/s11009-013-9392-1zbMath1322.60167OpenAlexW1982714915MaRDI QIDQ496968

Antonio Di Crescenzo, Shelemyahu Zacks

Publication date: 23 September 2015

Published in: Methodology and Computing in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11009-013-9392-1

zbMATH Keywords

modified Bessel functionstandard Brownian motionalternating counting processalternating driftErlang random timesexponential random timesgeneralized telegraph processtwo-index pseudo-Bessel function

Mathematics Subject Classification ID

Brownian motion (60J65) Markov renewal processes, semi-Markov processes (60K15) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (11)

Large deviations for some non-standard telegraph processes ⋮ Some results on the telegraph process driven by gamma components ⋮ \(\mathrm{M}/\mathrm{M}/1\) queue in two alternating environments and its heavy traffic approximation ⋮ Hypo-exponential distributions and compound Poisson processes with alternating parameters ⋮ Asymptotic results for the absorption time of telegraph processes with a non-standard barrier at the origin ⋮ Telegraph process with elastic boundary at the origin ⋮ Asymptotic results for the absorption time of telegraph processes with elastic boundary at the origin ⋮ On estimation for Brownian motion governed by telegraph process with multiple off states ⋮ Discretely observed Brownian motion governed by telegraph process: estimation ⋮ Probabilistic analysis of systems alternating for state-dependent dichotomous noise ⋮ On occupation time for on-off processes with multiple off-states

Cites Work

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• Simulation of first-passage times for alternating Brownian motions
• The Wiener disorder problem with finite horizon
• Probability law, flow function, maximum distribution of wave-governed random motions and their connections with Kirchhoff's laws
• Option pricing model based on a Markov-modulated diffusion with jumps
• On the Wiener disorder problem
• Hyperbolic equations arising in random models
• Brownian fluctuations in space-time with applications to vibrations of rods
• On random motions with velocities alternating at Erlang-distributed random times
• Least-squares change-point estimation for the telegraph process observed at discrete times
• Generalized Telegraph Process with Random Delays
• Wiener Disorder Problem with Observations at Fixed Discrete Time Epochs
• Option Pricing With Markov-Modulated Dynamics
• Effective Motion of a Virus Trafficking Inside a Biological Cell
• A Damped Telegraph Random Process with Logistic Stationary Distribution
• Pricing Options Under a Generalized Markov-Modulated Jump-Diffusion Model
• Oscillating Brownian motion
• Information and option pricings
• Total duration of negative surplus for the compound Poisson process that is perturbed by diffusion
• Generalized integrated telegraph processes and the distribution of related stopping times
• A jump telegraph model for option pricing
• A Double Band Control Policy of a Brownian Perishable Inventory System
• Estimating the Current Mean of a Normal Distribution which is Subjected to Changes in Time
• Probabilistic analysis of the telegrapher's process with drift by means of relativistic transformations

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