scholarly journals Marginal distributions of self-similar processes with stationary increments

1983 ◽  
Vol 64 (1) ◽  
pp. 129-138 ◽  
Author(s):  
George L. O'Brien ◽  
Wim Vervaat
Keyword(s):  
Marginal Distributions ◽  
Stationary Increments ◽  
Self Similar

scholarly journals Representations of hermite processes using local time of intersecting stationary stable regenerative sets

2020 ◽  
Vol 57 (4) ◽  
pp. 1234-1251
Author(s):  
Shuyang Bai
Keyword(s):  
Long Range ◽  
Local Time ◽  
Limit Theorems ◽  
Local Times ◽  
Long Range Dependence ◽  
Random Interval ◽  
Stationary Increments ◽  
Self Similar ◽  
Regenerative Sets

AbstractHermite processes are a class of self-similar processes with stationary increments. They often arise in limit theorems under long-range dependence. We derive new representations of Hermite processes with multiple Wiener–Itô integrals, whose integrands involve the local time of intersecting stationary stable regenerative sets. The proof relies on an approximation of regenerative sets and local times based on a scheme of random interval covering.

Stable Non-Gaussian Self-Similar Processes with Stationary Increments

2017 ◽  
Author(s):  
Vladas Pipiras ◽  
Murad S. Taqqu
Keyword(s):  
Stationary Increments ◽  
Self Similar ◽  
Non Gaussian

scholarly journals Two classes of self-similar stable processes with stationary increments

1989 ◽  
Vol 32 (2) ◽  
pp. 305-329 ◽  
Author(s):  
Stamatis Cambanis ◽  
Makoto Maejima
Keyword(s):  
Stable Processes ◽  
Stationary Increments ◽  
Self Similar

scholarly journals Stationary-increment Student and variance-gamma processes

2006 ◽  
Vol 43 (02) ◽  
pp. 441-453 ◽  
Author(s):  
Richard Finlay ◽  
Eugene Seneta
Keyword(s):  
Process Model ◽  
Asset Price ◽  
Continuous Time Model ◽  
Time Model ◽  
Variance Gamma ◽  
Stationary Increments ◽  
Gamma Distributions ◽  
Self Similar ◽  
Log Price ◽  
Gamma Processes

A continuous-time model with stationary increments for asset price {P t } is an extension of the symmetric subordinator model of Heyde (1999), and allows for skewness of returns. In the setting of independent variance-gamma-distributed returns the model resembles closely that of Madan, Carr, and Chang (1998). A simple choice of parameters renders {e−rt P t } a familiar martingale. We then specify the activity time process, {T t }, for which {T t − t} is asymptotically self-similar and {τ t }, with τ t = T t − T t−1, is gamma distributed. This results in a skew variance-gamma distribution for each log price increment (return) X t and a model for {X t } which incorporates long-range dependence in squared returns. Our approach mirrors that for the (symmetric) Student process model of Heyde and Leonenko (2005), to which the present work is intended as a complement and a sequel. One intention is to compare, partly on the basis of fitting to data, versions of the general model wherein the returns have either (symmetric) t-distributions or variance-gamma distributions.

Self-Affine Processes and the Ergodic Theorem

1994 ◽  
Vol 37 (2) ◽  
pp. 254-262 ◽  
Author(s):  
Wim Vervaat
Keyword(s):  
Ergodic Theorem ◽  
Sample Path ◽  
Stationary Increments ◽  
Affine Processes ◽  
Self Similar ◽  
The One

AbstractKnown results for strictly stable motions as finiteness of moments and local boundednessof sample-path variation are generalized to self-affine processes, i.e., self-similar processes with stationary increments. The proofs are new, even for stable motions, and are obtained by applying the ergodic theorem to powers of the (one-sided) increments.

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