Properties and applications of stochastic processes with stationary increments

1974 ◽  
Vol 6 (2) ◽  
pp. 205-207
Author(s):  
B. Picinbono
Keyword(s):  
Stochastic Processes ◽  
Stationary Increments

Properties and applications of stochastic processes with stationarynth-order increments

1974 ◽  
Vol 6 (3) ◽  
pp. 512-523 ◽  
Author(s):  
B. Picinbono
Keyword(s):  
Stochastic Processes ◽  
Stationary Process ◽  
General Description ◽  
Linear Filtering ◽  
Stationary Increments ◽  
Physical Problems

Many physical problems are described by stochastic processes with stationary increments. We present a general description of such processes. In particular we give an expression of a process in terms of its increments and we show that there are two classes of processes: diffusion and asymptotically stationary. Moreover, we show that thenth increments are given by a linear filtering of an arbitrary stationary process.

scholarly journals Condition for intersection occupation measure to be absolutely continuous

2020 ◽  
Vol 72 (9) ◽  
pp. 1304-1312
Author(s):  
X. Chen
Keyword(s):  
Stochastic Processes ◽  
Lebesgue Measure ◽  
Local Time ◽  
Minimal Condition ◽  
Occupation Measure ◽  
Absolutely Continuous ◽  
Intersection Local Time ◽  
Stationary Increments

UDC 519.21 Given the i.i.d. -valued stochastic processes with the stationary increments, a minimal condition is provided for the occupation measure to be absolutely continuous with respect to the Lebesgue measure on An isometry identity related to the resulting density (known as intersection local time) is also established.

scholarly journals On regular variation for infinitely divisible random vectors and additive processes

2006 ◽  
Vol 38 (01) ◽  
pp. 134-148 ◽  
Author(s):  
Henrik Hult ◽  
Filip Lindskog
Keyword(s):  
Stochastic Processes ◽  
Regular Variation ◽  
Tail Behavior ◽  
Random Vectors ◽  
Lévy Measure ◽  
Infinitely Divisible ◽  
Additive Process ◽  
Asymptotic Decay ◽  
Stationary Increments ◽  
Additive Processes

We study the tail behavior of regularly varying infinitely divisible random vectors and additive processes, i.e. stochastic processes with independent but not necessarily stationary increments. We show that the distribution of an infinitely divisible random vector is tail equivalent to its Lévy measure and we study the asymptotic decay of the probability for an additive process to hit sets far away from the origin. The results are extensions of known univariate results to the multivariate setting; we exemplify some of the difficulties that arise in the multivariate case.

Generalized Lorenz curves and convexifications of stochastic processes

2003 ◽  
Vol 40 (04) ◽  
pp. 906-925 ◽  
Author(s):  
Youri Davydov ◽  
Ričardas Zitikis
Keyword(s):  
Stochastic Processes ◽  
Limit Theorems ◽  
Asymptotic Theory ◽  
Fixed Time ◽  
Weak Limit ◽  
Time Intervals ◽  
Lorenz Curves ◽  
Stationary Increments ◽  
Weak Limit Theorems ◽  
Vervaat Process

We investigate convex rearrangements, called convexifications for brevity, of stochastic processes over fixed time intervals and develop the corresponding asymptotic theory when the time intervals indefinitely expand. In particular, we obtain strong and weak limit theorems for these convexifications when the processes are Gaussian with stationary increments and then illustrate the results using fractional Brownian motion. As a theoretical basis for these investigations, we extend some known, and also obtain new, results concerning the large sample asymptotic theory for the empirical generalized Lorenz curves and the Vervaat process when observations are stationary and either short-range or long-range dependent.

Sign in / Sign up

Export Citation Format

Share Document