A note on functions of Markov processes with an application to a sequence of χ2 statistics

1973 ◽  
Vol 10 (4) ◽  
pp. 895-900
Author(s):  
Murray A. Cameron
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Joint Distribution ◽  
Sufficient Condition ◽  
Simple Derivation ◽  
Reverse Process

A sufficient condition for a function of a Markov process to be Markovian is obtained by considering a reverse process of the original Markov process. An application of this result provides a simple derivation of the joint distribution of a sequence of Pearson χ2 statistics previously obtained by Zaharov, Sarmanov and Sevast'ianov (1969).

A note on functions of Markov processes with an application to a sequence of χ2 statistics

1973 ◽  
Vol 10 (04) ◽  
pp. 895-900
Author(s):  
Murray A. Cameron
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Joint Distribution ◽  
Sufficient Condition ◽  
Simple Derivation ◽  
Reverse Process

A sufficient condition for a function of a Markov process to be Markovian is obtained by considering a reverse process of the original Markov process. An application of this result provides a simple derivation of the joint distribution of a sequence of Pearson χ 2 statistics previously obtained by Zaharov, Sarmanov and Sevast'ianov (1969).

scholarly journals Monounireducible Nonhomogeneous Continuous Time Semi-Markov Processes Applied to Rating Migration Models

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Guglielmo D'Amico ◽  
Jacques Janssen ◽  
Raimondo Manca
Keyword(s):  
Distribution Function ◽  
Markov Process ◽  
Markov Processes ◽  
Continuous Time ◽  
Topological Structure ◽  
Credit Rating ◽  
Fundamental Importance ◽  
Sufficient Condition ◽  
Semi Markov Process ◽  
Semi Markov Processes

Monounireducible nonhomogeneous semi- Markov processes are defined and investigated. The mono- unireducible topological structure is a sufficient condition that guarantees the absorption of the semi-Markov process in a state of the process. This situation is of fundamental importance in the modelling of credit rating migrations because permits the derivation of the distribution function of the time of default. An application in credit rating modelling is given in order to illustrate the results.

On occupation times for quasi-Markov processes

1981 ◽  
Vol 18 (01) ◽  
pp. 297-301 ◽  
Author(s):  
Lennart Bondesson
Keyword(s):  
Markov Process ◽  
Laplace Transform ◽  
Markov Processes ◽  
Joint Distribution ◽  
Stieltjes Transform ◽  
Occupation Times ◽  
The Laplace Transform ◽  
The Times

In this note the joint distribution for the times in an interval [0, t] spent in the states 1, 2, ···, N in a standard quasi-Markov process of order N is considered. An expression for the Laplace transform with respect to t of the Laplace–Stieltjes transform of this joint distribution is derived.

On occupation times for quasi-Markov processes

1981 ◽  
Vol 18 (1) ◽  
pp. 297-301 ◽  
Author(s):  
Lennart Bondesson
Keyword(s):  
Markov Process ◽  
Laplace Transform ◽  
Markov Processes ◽  
Joint Distribution ◽  
Stieltjes Transform ◽  
Occupation Times ◽  
The Laplace Transform ◽  
The Times

In this note the joint distribution for the times in an interval [0, t] spent in the states 1, 2, ···, N in a standard quasi-Markov process of order N is considered. An expression for the Laplace transform with respect to t of the Laplace–Stieltjes transform of this joint distribution is derived.

scholarly journals Financial Applications of Bivariate Markov Processes

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Sergio Ortobelli Lozza ◽  
Enrico Angelelli ◽  
Annamaria Bianchi
Keyword(s):  
Risk Management ◽  
Markov Chain ◽  
Markov Process ◽  
Option Pricing ◽  
Markov Processes ◽  
Joint Distribution ◽  
Large Scale ◽  
Portfolio Theory ◽  
Asian Options ◽  
Financial Applications

This paper describes a methodology to approximate a bivariate Markov process by means of a proper Markov chain and presents possible financial applications in portfolio theory, option pricing and risk management. In particular, we first show how to model the joint distribution between market stochastic bounds and future wealth and propose an application to large-scale portfolio problems. Secondly, we examine an application to VaR estimation. Finally, we propose a methodology to price Asian options using a bivariate Markov process.

Replacement of train wheels: an application of dynamic reversal of a Markov process

1994 ◽  
Vol 31 (01) ◽  
pp. 1-8
Author(s):  
David Gates ◽  
Mark Westcott
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Time Reversal ◽  
Equilibrium Distribution ◽  
Natural Extension ◽  
Product Form ◽  
Simple Derivation ◽  
Original Process ◽  
Population Process ◽  
Ordinary Time

A problem of regrinding and recycling worn train wheels leads to a Markov population process with distinctive properties, including a product-form equilibrium distribution. A convenient framework for analyzing this process is via the notion of dynamic reversal, a natural extension of ordinary (time) reversal. The dynamically reversed process is of the same type as the original process, which allows a simple derivation of some important properties. The process seems not to belong to any class of Markov processes for which stationary distributions are known.

Replacement of train wheels: an application of dynamic reversal of a Markov process

1994 ◽  
Vol 31 (1) ◽  
pp. 1-8
Author(s):  
David Gates ◽  
Mark Westcott
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Time Reversal ◽  
Equilibrium Distribution ◽  
Natural Extension ◽  
Product Form ◽  
Simple Derivation ◽  
Original Process ◽  
Population Process ◽  
Ordinary Time

A problem of regrinding and recycling worn train wheels leads to a Markov population process with distinctive properties, including a product-form equilibrium distribution. A convenient framework for analyzing this process is via the notion of dynamic reversal, a natural extension of ordinary (time) reversal. The dynamically reversed process is of the same type as the original process, which allows a simple derivation of some important properties. The process seems not to belong to any class of Markov processes for which stationary distributions are known.

scholarly journals CLASSICAL MARKOV PROCESSES FROM QUANTUM LÉVY PROCESSES

1999 ◽  
Vol 02 (01) ◽  
pp. 105-129 ◽  
Author(s):  
UWE FRANZ
Keyword(s):  
Markov Process ◽  
Hopf Algebra ◽  
Markov Processes ◽  
Lévy Processes ◽  
Sufficient Conditions ◽  
Markov Property ◽  
Vacuum State ◽  
Levy Processes ◽  
Quantum Process ◽  
Quantum Markov Processes

We show how classical Markov processes can be obtained from quantum Lévy processes. It is shown that quantum Lévy processes are quantum Markov processes, and sufficient conditions for restrictions to subalgebras to remain quantum Markov processes are given. A classical Markov process (which has the same time-ordered moments as the quantum process in the vacuum state) exists whenever we can restrict to a commutative subalgebra without losing the quantum Markov property.8 Several examples, including the Azéma martingale, with explicit calculations are presented. In particular, the action of the generator of the classical Markov processes on polynomials or their moments are calculated using Hopf algebra duality.

A temporal factorization at the maximum for certain positive self-similar Markov processes

2020 ◽  
Vol 57 (4) ◽  
pp. 1045-1069
Author(s):  
Matija Vidmar
Keyword(s):  
Markov Process ◽  
Laplace Transform ◽  
Markov Processes ◽  
Absorption Time ◽  
The Laplace Transform ◽  
Self Similar

AbstractFor a spectrally negative self-similar Markov process on $[0,\infty)$ with an a.s. finite overall supremum, we provide, in tractable detail, a kind of conditional Wiener–Hopf factorization at the maximum of the absorption time at zero, the conditioning being on the overall supremum and the jump at the overall supremum. In a companion result the Laplace transform of this absorption time (on the event that the process does not go above a given level) is identified under no other assumptions (such as the process admitting a recurrent extension and/or hitting zero continuously), generalizing some existing results in the literature.

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