레비 확률 과정

노트

위키데이터

• ID : Q1557613

말뭉치

1. Informally speaking, a Lévy process is a random trajectory, generalizing the concept of Brownian motion, which may contain jump discontinuities.
2. The terms of this triplet suggest that a Lévy process can be seen as having three independent components: a linear drift, a Brownian motion, and a Lévy jump process, as described below.
3. Khintchine theorem suggests that every Lévy process is the sum of Brownian motion with drift and another independent random variable.
4. t≥0 be a free Lévy process (in law) affiliated with aW*-probability space (𝒜, τ) and with marginal distributions (μ t ).
5. t≥0 is termed the background driving Lévy process or the BDLP corresponding to Y; this is due to its role for processes of Ornstein–Uhlenbeck type (see ref. 16).
6. Now choose a free Lévy process (Z t ) affiliated with some W*-probability space (𝒜′, τ′) and corresponding to (X t ) as in Proposition 1.2.
7. In order to describe precisely the sum of jumps of a Lévy process, one needs to introduce the concept of Poisson random measures.
8. The distributions that can appear as the distribution of the instantaneous value of a homogeneous Lévy process are exactly those that have the property called infinite divisibility.
9. The fact that a Lévy process τ exists such that τ(1) is generalized inverse Gaussian distributed follows because these distributions are infinitely divisible, as mentioned in Section 1.
10. This model is the generalized hyperbolic Lévy process with a gamma mixing distribution.
11. A theory of the term structure of interest rates based on the hyperbolic Lévy process was developed in Eberlein and Raible (1999).
12. In this paper we compute equivalent martingale measures when the asset price returns are modelled by a Lévy process.
13. Moreover, the original process is still a Lévy process under this new probability and is called the Esscher transform of the original process.
14. and we consider a Lévy process with the following triplet (0,0, P ).
15. In this paper we have used a Lévy process to model asset price returns, which allow us to capture more stylized facts from real data.
16. This Demonstration shows the path of a symmetric stable Lévy process.
17. For , the stable Lévy process coincides with ordinary Brownian motion.
18. A strictly stable Lévy process can be viewed as a generalization of Brownian motion, and has the property for all , , has the same distribution as , for some index of stability , where .
19. This method allows the residual to submit to a Lévy process.
20. In this part, a dynamic asset distribution evolution process based on Lévy process and asymmetrical heteroscedastic process is built.
21. We assume that the residual in (1) submits to infinite-jump Lévy process and it is recorded as .
22. Infinite-jump Lévy process usually has three characteristic items, , , and , representing linear drift, Brownian motion diffusion, and jump, respectively.
23. More generally, it is possible to define the notion of a Lévy process with respect to a given filtered probability space .
24. In particular, if X is a Lévy process according to definition 1 then it is also a Lévy process with respect to its natural filtration .
25. The most common example of a Lévy process is Brownian motion, where is normally distributed with zero mean and variance independently of .
26. This is called a Cauchy process, which is a purely discontinuous Lévy process.
27. A typical model is obtained by considering finite dimensional linear stochastic SISO systems driven by a Levy process.
28. In this paper we consider a discrete-time version of this model driven by the increments of a Levy process, such a system will be called Levy system.