On Stochastic Approximation for Random Processes with Continuous Time

1971 ◽  
Vol 16 (4) ◽  
pp. 674-682 ◽  
Author(s):  
T. P. Krasulina
Keyword(s):  
Stochastic Approximation ◽  
Continuous Time ◽  
Random Processes

Stochastic ordering of random processes with an imbedded point process

1991 ◽  
Vol 28 (3) ◽  
pp. 553-567 ◽  
Author(s):  
François Baccelli
Keyword(s):  
Point Process ◽  
Continuous Time ◽  
Random Sequence ◽  
Stochastic Ordering ◽  
Random Processes ◽  
Time Process ◽  
Continuous Time Process ◽  
Partial Orderings ◽  
Stationary Probabilities

We introduce multivariate partial orderings related with the Palm and time-stationary probabilities of a point process. Using these orderings, we give conditions for the monotonicity of a random sequence, with respect to some integral stochastic ordering, to be inherited with a continuous time process in which this sequence is imbedded. This type of inheritance is also discussed for the property of association.

Wiener-Hopf methods, decompositions, and factorisation identities for maxima and minima of homogeneous random processes

1975 ◽  
Vol 7 (04) ◽  
pp. 767-785 ◽  
Author(s):  
Priscilla Greenwood
Keyword(s):  
Integral Equation ◽  
Random Walk ◽  
Continuous Time ◽  
Random Processes ◽  
Lévy Measure ◽  
Random Walk Method ◽  
Process Decomposition

Some Wiener-Hopf type results are collected, related and given more direct proofs. Spitzer's random-walk method for the Wiener-Hopf integral equation also produces his factorisation relating functionals of maxima and minima. Transform equations are interpreted as decompositions of time-changed processes. Discrete- and continuous-time versions are related. Prabhu's factorisation for generators is equivalent to Fristedt's Lévy measure factorisation and to process decomposition.

scholarly journals A simple approach in limit theorems for linear random processes and fields with continuous time

2012 ◽  
Vol 57 (4) ◽  
pp. 724-743
Author(s):  
Юрий Александрович Давыдов ◽  
Yurii Aleksandrovich Davydov ◽  
Вигантас И Паулаускас ◽  
Vygantas I Paulauskas
Keyword(s):  
Continuous Time ◽  
Limit Theorems ◽  
Random Processes ◽  
Simple Approach

A relatively quick way to simulate local random processes on a lattice

1998 ◽  
Vol 35 (03) ◽  
pp. 770-775
Author(s):  
Daniel Richardson ◽  
Wayne Burton
Keyword(s):  
Exponential Distribution ◽  
Dynamic Simulation ◽  
Markov Processes ◽  
Continuous Time ◽  
Growth Process ◽  
Computation Time ◽  
Random Processes ◽  
Random Growth ◽  
Transition Rules ◽  
Local Transition

A class of Markov processes in continuous time, with local transition rules, acting on colourings of a lattice, is defined. An algorithm is described for dynamic simulation of such processes. The computation time for the next state is O(logb), where b is the number of possible next states. This technique is used to give some evidence that the limiting shape for a random growth process in the plane with exponential distribution is approximately a circle.

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