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2015
This chapter considers jump-diffusion processes to allow for price fluctuations to have two components, one consisting of the usual increments of a Wiener process, the second allows for “large” jumps from time-to-time. We introduce Poisson jump process with either absolute or proportional jump sizes through the stochastic integrals and provide ...
Carl Chiarella +2 more
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This chapter considers jump-diffusion processes to allow for price fluctuations to have two components, one consisting of the usual increments of a Wiener process, the second allows for “large” jumps from time-to-time. We introduce Poisson jump process with either absolute or proportional jump sizes through the stochastic integrals and provide ...
Carl Chiarella +2 more
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2021
In this chapter the aim is to describe those jump processes that form the building blocks for most modeling. All of these can be described by integer variables.
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In this chapter the aim is to describe those jump processes that form the building blocks for most modeling. All of these can be described by integer variables.
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Harnack Inequalities for Jump Processes
Potential Analysis, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bass, Richard F., Levin, David A.
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Optimal Control of Jump Processes
SIAM Journal on Control and Optimization, 1977The paper proposes an abstract model for the problem of optimal control of systems subject to random perturbations, for which the principle of optimality takes on an appealing form. This model is specialized to the case where the state of the controlled system is realized as a jump process.
Boel, R., Varaiya, P.
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2003
The importance of Markov jump processes for queueing theory is obvious. On the one hand, in stochastic modelling the use of Markov processes makes an analysis of the models much easier. On the other hand, for the number of users in a queueing system a mathematical model must be a jump process. The combination of these, i.e.
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The importance of Markov jump processes for queueing theory is obvious. On the one hand, in stochastic modelling the use of Markov processes makes an analysis of the models much easier. On the other hand, for the number of users in a queueing system a mathematical model must be a jump process. The combination of these, i.e.
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Proceedings of 27th Asilomar Conference on Signals, Systems and Computers, 2002
Using a change of measure a filtering problem is discussed where both the signal and observation processes are diffusions with jumps. >
R.J. Elliott, L. Aggoun
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Using a change of measure a filtering problem is discussed where both the signal and observation processes are diffusions with jumps. >
R.J. Elliott, L. Aggoun
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On Markov-Additive Jump Processes
Queueing Systems, 2002The focus is on Markov-additive processes, which belong to the class of Markov jump processes. Markov-additive jump processes are defined as 2-dimensional Markov jump processes, which satisfy the condition that the transition probabilities depend on one dimension only.
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2019
In this chapter we introduce jump-diffusion processes and provide a theoretical framework that justifies the nonparametric (data-based) extraction of the parameters and functions controlling the arrival of a jump and the distribution of the jump size from the estimated conditional Kramers–Moyal moments. The method and the results are applicable to both
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In this chapter we introduce jump-diffusion processes and provide a theoretical framework that justifies the nonparametric (data-based) extraction of the parameters and functions controlling the arrival of a jump and the distribution of the jump size from the estimated conditional Kramers–Moyal moments. The method and the results are applicable to both
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1993
We want to describe Markov processes that evolve through continuous time t ≥ 0, but in a discrete state space ℒ. The prescription for such a process has two ingredients. There are random jump times 0 < τ1 < τ2 < … < τn < … when the process jumps away from the state it is at, and there are transition probabilities Q xy that govern the transitions at ...
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We want to describe Markov processes that evolve through continuous time t ≥ 0, but in a discrete state space ℒ. The prescription for such a process has two ingredients. There are random jump times 0 < τ1 < τ2 < … < τn < … when the process jumps away from the state it is at, and there are transition probabilities Q xy that govern the transitions at ...
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Jump Processes and Boundary Processes
1984Publisher Summary This chapter discusses the jump processes and boundary processes. The chapter describes the development of the Malliavin calculus by Malliavin. Another approach to the calculus of variations on jump processes is discussed. It is based on more elementary arguments, and does not rely on the Girsanov transformation on jump processes ...
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