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.

Properties and applications of stochastic processes with stationary nth-order increments

1974 ◽  
Vol 6 (03) ◽  
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 the central limit theorem and iterated logarithm law for stationary processes

1975 ◽  
Vol 12 (1) ◽  
pp. 1-8 ◽  
Author(s):  
C.C. Heyde
Keyword(s):  
Central Limit ◽  
Stationary Process ◽  
Stationary Processes ◽  
Martingale Differences ◽  
Stationary Increments ◽  
The Central Limit Theorem ◽  
Iterated Logarithm ◽  
Logarithm Law ◽  
Functional Forms ◽  
Iterated Logarithm Law

It has recently emerged that a convenient way to establish central limit and iterated logarithm results for processes with stationary increments is to use approximating martingales with stationary increments. Functional forms of the limit results can be obtained via a representation for the increments of the stationary process in terms of stationary martingale differences plus other terms whose sum telescopes and disappears under suitable norming. Results based on the most general form of such a representation are here obtained.

A uniqueness problem for the envelope of an oscillatory process

1979 ◽  
Vol 16 (04) ◽  
pp. 822-829
Author(s):  
A. M. Hasofer
Keyword(s):  
Stochastic Processes ◽  
Stationary Process ◽  
Transient Processes ◽  
Uniqueness Problem ◽  
Oscillatory Process ◽  
Linear Filter ◽  
Time Varying ◽  
Definition Of ◽  
Oscillatory Processes

In a previous paper, the author has described a method for obtaining envelope processes for oscillatory stochastic processes. These are processes which can be represented as the output of a time-varying linear filter whose input is a stationary process. It is shown in this paper that the proposed definition of the envelope process may not be unique, but may depend on the particular representation of the oscillatory process chosen. It is then shown that for a class of oscillatory processes which is of particular interest, the class of transient processes, there is a class of natural representations which all lead to a unique envelope process.

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