Orderliness, intensities and Palm-Khinchin equations for multivariate point processes

1975 ◽  
Vol 12 (2) ◽  
pp. 383-389 ◽  
Author(s):  
D. J. Daley ◽  
R. K. Milne
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Multivariate Point ◽  
Multivariate Point Processes

Simple definitions and derivations of elementary properties are given for the various intensities and Palm-Khinchin functions associated with a multivariate point process.

Learning models with continuous time parameter and multivariate point processes

1983 ◽  
Vol 20 (4) ◽  
pp. 884-890 ◽  
Author(s):  
Helmut Pruscha
Keyword(s):  
Point Process ◽  
Continuous Time ◽  
Point Processes ◽  
Transition Probabilities ◽  
Learning Model ◽  
Time Parameter ◽  
Learning Models ◽  
Random System ◽  
Multivariate Point ◽  
Multivariate Point Processes

The concept of a learning model (or random system with complete connections) with continuous time parameter is introduced on the basis of the notion of a multivariate point process possessing an intensity. The stepwise transition probabilities in terms of the intensity are derived and a Monte Carlo method for simulating a sample is presented. By modelling the intensity process various types of learning models can be built. We propose a linear learning model which comprises the continuous-time Markov process as well as Hawkes's mutually exciting point process. We study the asymptotic behaviour of this linear model in terms of explosion or extinction and of convergence of some estimates. We close with some numerical results from computer simulations.

Orderliness, intensities and Palm-Khinchin equations for multivariate point processes

1975 ◽  
Vol 12 (02) ◽  
pp. 383-389 ◽  
Author(s):  
D. J. Daley ◽  
R. K. Milne
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Multivariate Point ◽  
Multivariate Point Processes

Simple definitions and derivations of elementary properties are given for the various intensities and Palm-Khinchin functions associated with a multivariate point process.

Learning models with continuous time parameter and multivariate point processes

1983 ◽  
Vol 20 (04) ◽  
pp. 884-890
Author(s):  
Helmut Pruscha
Keyword(s):  
Point Process ◽  
Continuous Time ◽  
Point Processes ◽  
Transition Probabilities ◽  
Learning Model ◽  
Time Parameter ◽  
Learning Models ◽  
Random System ◽  
Multivariate Point ◽  
Multivariate Point Processes

The concept of a learning model (or random system with complete connections) with continuous time parameter is introduced on the basis of the notion of a multivariate point process possessing an intensity. The stepwise transition probabilities in terms of the intensity are derived and a Monte Carlo method for simulating a sample is presented. By modelling the intensity process various types of learning models can be built. We propose a linear learning model which comprises the continuous-time Markov process as well as Hawkes's mutually exciting point process. We study the asymptotic behaviour of this linear model in terms of explosion or extinction and of convergence of some estimates. We close with some numerical results from computer simulations.

Point-Process Principal Components Analysis via Geometric Optimization

2013 ◽  
Vol 25 (1) ◽  
pp. 101-122 ◽  
Author(s):  
Victor Solo ◽  
Syed Ahmed Pasha
Keyword(s):  
Principal Components Analysis ◽  
Point Process ◽  
Principal Components ◽  
Neural Coding ◽  
Point Processes ◽  
Geometric Optimization ◽  
Process Data ◽  
Components Analysis ◽  
Point Process Data ◽  
Multivariate Point

There has been a fast-growing demand for analysis tools for multivariate point-process data driven by work in neural coding and, more recently, high-frequency finance. Here we develop a true or exact (as opposed to one based on time binning) principal components analysis for preliminary processing of multivariate point processes. We provide a maximum likelihood estimator, an algorithm for maximization involving steepest ascent on two Stiefel manifolds, and novel constrained asymptotic analysis. The method is illustrated with a simulation and compared with a binning approach.

scholarly journals Multivariate General Compound Point Processes in Limit Order Books

Risks ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 98
Author(s):  
Qi Guo ◽  
Bruno Remillard ◽  
Anatoliy Swishchuk
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Hawkes Process ◽  
Limit Order ◽  
Large Numbers ◽  
Order Books ◽  
Limit Order Books ◽  
Functional Central Limit Theorems ◽  
Multivariate Point ◽  
Functional Central Limit

In this paper, we focus on a new generalization of multivariate general compound Hawkes process (MGCHP), which we referred to as the multivariate general compound point process (MGCPP). Namely, we applied a multivariate point process to model the order flow instead of the Hawkes process. The law of large numbers (LLN) and two functional central limit theorems (FCLTs) for the MGCPP were proved in this work. Applications of the MGCPP in the limit order market were also considered. We provided numerical simulations and comparisons for the MGCPP and MGCHP by applying Google, Apple, Microsoft, Amazon, and Intel trading data.

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