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Singularities of the matrix exponent of a Markov additive process with one-sided jumps

Jevgenijs Ivanovs, Onno Boxma, Michel Mandjes
2010 Stochastic Processes and their Applications  
Singularities of the matrix exponent of a Markov additive process with one-sided jumps Ivanovs, J.; Boxma, O.; Mandjes, M.R.H.  ...  Abstract We analyze the number of zeros of det(F(α)), where F(α) is the matrix exponent of a Markov Additive Process (MAP) with one-sided jumps.  ...  Introduction In this paper we consider Markov Additive Processes (MAPs) with one-sided jumps.  ... 
doi:10.1016/j.spa.2010.05.007 fatcat:prywionaargxpjl7bsmkevba6y

Extremes of Markov-additive Processes with One-sided Jumps, with Queueing Applications

A. B. Dieker, M. Mandjes
2009 Methodology and Computing in Applied Probability  
Through Laplace transforms, we study the extremes of a continuoustime Markov-additive process with one-sided jumps and a finite-state background Markovian state-space, jointly with the epoch at which the  ...  For this, we investigate discrete-time Markov-additive processes and use an embedding to relate these to the continuous-time setting.  ...  Phase-type Jumps in the Opposite Direction All Markov-additive processes in this paper have one-sided jumps.  ... 
doi:10.1007/s11009-009-9140-8 fatcat:lgk47pj26nfrvoll7cobcce7bm

Markov-Additive Jump Processes [chapter]

Lothar Breuer
2003 From Markov Jump Processes to Spatial Queues  
Furthermore, the class of Markov-additive jump processes introduced in the present paper is embedded into the existing theory of jump processes.  ...  In 1995, Pacheco and Prabhu introduced the class of so-called Markov-additive processes of arrivals in order to provide a general class of arrival processes for queueing theory.  ...  In the present paper, the focus is on Markov-additive processes which belong to the class of Markov jump processes.  ... 
doi:10.1007/978-94-010-0239-4_2 fatcat:zwbp6vkhmzfwfdh4xhodmvdgum

A characterization of Markov solutions for stochastic differential equations with jumps [chapter]

Anne Estrade
1997 Lecture notes in mathematics  
It is also close in spirit to theorem 6.27 of [2] where the local characteristics of an additive semimartingale based on a Markov process are described.  ...  We choose as a candidate for our additive process on (, , t, Px) the following : On the other hand, ~4 is clearly additive and so also satisfies condition (x) of prop. 1.  ... 
doi:10.1007/bfb0119316 fatcat:a3jazfflcncyllhysdfiiyww6e

Explicit Causal Recursive Estimators for Continuous-Time Bivariate Markov Chains

Brian L. Mark, Yariv Ephraim
2014 IEEE Transactions on Signal Processing  
We develop explicit causal recursions for estimating the number of jumps from one state to another, and the total sojourn time in each state, of a general bivariate Markov chain.  ...  One of the two processes is observable, while the other is an underlying process which affects the statistical properties of the observable process.  ...  Each of the two processes comprising the bivariate Markov chain need not be Markov, and the two processes may jump simultaneously. Only one of these two processes is assumed observable.  ... 
doi:10.1109/tsp.2014.2314434 fatcat:i2o4cugyezd55iwoqpvsjyn6ei

An EM Algorithm for Markov Modulated Markov Processes

Y. Ephraim, W.J.J. Roberts
2009 IEEE Transactions on Signal Processing  
Conditioned on that chain, the observable process is a continuous-time finite-state nonhomogeneous Markov chain.  ...  An expectation-maximization (EM) algorithm for estimating the parameter of a Markov modulated Markov process in the maximum likelihood sense is developed.  ...  The density of the observable process on the space of sample functions may be evaluated as follows. Assume that the process jumps times in . Suppose first that the last jump occurs at .  ... 
doi:10.1109/tsp.2008.2007919 fatcat:ndtcmrvhxzfa5gekz2jbhb463u

Kolmogorov's Equations for Jump Markov Processes and their Applications to Control Problems [article]

Eugene A. Feinberg, Albert N. Shiryaev
2021 arXiv   pre-print
This paper describes the structure of solutions to Kolmogorov's equations for nonhomogeneous jump Markov processes and applications of these results to control of jump stochastic systems.  ...  These equations were studied by Feller (1940), who clarified in 1945 in the errata to that paper that some of its results covered only nonexplosive Markov processes.  ...  By defdinition, a jump Markov process is a Markov process which is also a jump process. 2.3.  ... 
arXiv:2109.05079v2 fatcat:ls33kjnck5h3jf7rt6zalo7dqa

Page 453 of American Mathematical Society. Transactions of the American Mathematical Society Vol. 82, Issue 2 [page]

1956 American Mathematical Society. Transactions of the American Mathematical Society  
Feller has suggested that for transition probabilities satisfying Ao, the additional hypothesis By is equivalent to the proposition that for every initial distribution a Markov process can be formed from  ...  except for jumps from + and satisfying the strong Markov property.  ... 

The absence of arbitrage on the complete Black-Scholes-Merton regime-switching Lévy market

Anna Sulima
2021 Econometrics  
In the considered model, the prices of financial assets are described by the Lévy process in which the coefficients depend on the states of the Markov chain.  ...  In the regime-switching models, or Markov-modulated models, the coefficients depend on the Markov chain and change when the state of the chain alters.  ...  The Markov additive processes combine Levy processes with those modelled by the Markov chain, but other types of jumps also appear. This study checked whether the market is free from arbitrage.  ... 
doi:10.15611/eada.2021.3.04 fatcat:kxt6r7unavdbxmfqvkrds7hpt4

A note on chaotic and predictable representations for Itô-Markov additive processes [article]

Zbigniew Palmowski, Łukasz Stettner, Anna Sulima
2017 arXiv   pre-print
This family of processes includes Markov modulated Itô-Lévy processes and Markov additive processes.  ...  IIn this paper we provide predictable and chaotic representations for Itô-Markov additive processes X.  ...  Itô-Markov additive processes are a natural generalization of Itô-Lévy processes and thus of Lévy processes. Moreover, if γ(s, x) = x then X is a Markov additive process.  ... 
arXiv:1612.09216v2 fatcat:n4yngcwc7zhcraodxhks6zqqha

Page 740 of Mathematical Reviews Vol. 31, Issue 4 [page]

1966 Mathematical Reviews  
E. 4088 Incomplete discontinuous Markov J. Appl. Probability 2 (1965), 69-78. Markov processes with several classes of jumps are’ con- sidered.  ...  Motoo, Minoru 4087 The sweeping-out of additive functionals and processes on the bo Ann. Inst. Statist. Math. 16 (1964), 317-345.  ... 

Page 2306 of Mathematical Reviews Vol. , Issue 2004c [page]

2004 Mathematical Reviews  
It is divided into three parts: A Closer Look into Theory, which is about Markov jump processes and Markov-additive jump processes; Classical Queues, which defines the batch Markovian arrival process and  ...  Partic- ular attention is given to non-homogeneous processes with transi- tion rates which are periodic in time. Chapter 2 goes on to define Markov additive jump processes (MAJPs).  ... 

Page 3006 of Mathematical Reviews Vol. , Issue 96e [page]

1996 Mathematical Reviews  
However, for some choices of the a’s and b’s, it is possible for a 60 PROBABILITY THEORY AND STOCHASTIC PROCESSES 3006 the process to take infinitely many jumps in finite time, and one can ask for additional  ...  Similarly, if the process takes infinitely many “departing” jumps in finite time, it will actually leave the state space, and additional parameters are needed to describe its post-exit behavior.  ... 

Continuous Time Discounted Jump Markov Decision Processes: A Discrete-Event Approach

Eugene A. Feinberg
2004 Mathematics of Operations Research  
This paper introduces and develops a new approach to the theory of continuous time jump Markov decision processes (CTJMDP).  ...  This approach reduces discounted CTJMDPs to discounted semi-Markov decision processes (SMDPs) and eventually to discrete-time Markov decision processes (MDPs).  ...  We introduce a new approach to discounted continuous-time jump Markov decision processes (CTJMDPs).  ... 
doi:10.1287/moor.1040.0089 fatcat:i7huh3pguvbonpynd4rv3shoxy

Optimal control of noisy finite-state Markov processes

A. Segall
1977 IEEE Transactions on Automatic Control  
Two types of noisy observations are considered: additive white Gaussian noise and jump-type observations.  ...  The paper treats the problem of optimal control of finite-state Markov processes observed in noise.  ...  The Markov process had two components, one which was perfectly observable and one -5which could be observed only through a point process, the rate of which was modulated by the Markov process.  ... 
doi:10.1109/tac.1977.1101447 fatcat:cufqwxnrcvb2rposp443bfxifm
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