Asymptotic properties of integral functionals of geometric stochastic processes

2000 ◽  
Vol 37 (02) ◽  
pp. 480-493
Author(s):  
Endre Csáki ◽  
Miklós Csörgő ◽  
Antónia Földes ◽  
Pál Révész
Keyword(s):  
Stochastic Processes ◽  
Asymptotic Properties ◽  
Integral Functionals ◽  
Strong Invariance ◽  
Financial Modelling ◽  
Selection Of ◽  
General Conditions

We study strong asymptotic properties of two types of integral functionals of geometric stochastic processes. These integral functionals are of interest in financial modelling, yielding various option pricings, annuities, etc., by appropriate selection of the processes in their respective integrands. We show that under fairly general conditions on the latter processes the logs of the integral functionals themselves asymptotically behave like appropriate sup functionals of the processes in the exponents of their respective integrands. We illustrate the possible use and applications of these strong invariance theorems by listing and elaborating on several examples.

Asymptotic properties of integral functionals of geometric stochastic processes

2000 ◽  
Vol 37 (2) ◽  
pp. 480-493
Author(s):  
Endre Csáki ◽  
Miklós Csörgő ◽  
Antónia Földes ◽  
Pál Révész
Keyword(s):  
Stochastic Processes ◽  
Asymptotic Properties ◽  
Integral Functionals ◽  
Strong Invariance ◽  
Financial Modelling ◽  
Selection Of ◽  
General Conditions

We study strong asymptotic properties of two types of integral functionals of geometric stochastic processes. These integral functionals are of interest in financial modelling, yielding various option pricings, annuities, etc., by appropriate selection of the processes in their respective integrands. We show that under fairly general conditions on the latter processes the logs of the integral functionals themselves asymptotically behave like appropriate sup functionals of the processes in the exponents of their respective integrands. We illustrate the possible use and applications of these strong invariance theorems by listing and elaborating on several examples.

scholarly journals Perpetual integral functionals of multidimensional stochastic processes

Stochastics ◽  
2021 ◽  
pp. 1-12
Author(s):  
Yuri Kondratiev ◽  
Yuliya Mishura ◽  
José L. da Silva
Keyword(s):  
Stochastic Processes ◽  
Integral Functionals

Measuring the Velocity of a Signal

1975 ◽  
Vol 12 (S1) ◽  
pp. 227-237
Author(s):  
E. J. Hannan
Keyword(s):  
Plane Wave ◽  
Asymptotic Properties ◽  
General Conditions

The problem considered is that of measuring the velocity of a signal, constituted by a plane wave, from measurements at a number of recorders receiving noise as well as signal. The asymptotic properties of the estimates are considered under rather general conditions on the noise and signal processes.

Asymptotic properties and equilibrium conditions for branching Poisson processes

1969 ◽  
Vol 6 (02) ◽  
pp. 355-371 ◽  
Author(s):  
P.A.W. Lewis
Keyword(s):  
Normal Distribution ◽  
Initial Conditions ◽  
Asymptotic Properties ◽  
Poisson Processes ◽  
Asymptotic Results ◽  
Equilibrium Conditions ◽  
Equilibrium Processes ◽  
Equilibrium Process ◽  
Unit Normal ◽  
General Conditions

Some previously obtained asymptotic results for branching Poisson processes are extended and sharpened. It is shown that under rather general conditions the number of events in both the transient and the equilibrium processes, suitably normalized, have a unit normal distribution. Finally, unique initial conditions are derived for the equilibrium process.

Asymptotic properties of intensity estimators for Poisson shot-noise processes

1991 ◽  
Vol 28 (03) ◽  
pp. 568-583
Author(s):  
Friedrich Liese ◽  
Volker Schmidt
Keyword(s):  
Asymptotic Normality ◽  
Stochastic Processes ◽  
Point Process ◽  
Shot Noise ◽  
Poisson Point Process ◽  
Asymptotic Properties ◽  
Weak Consistency ◽  
Long Run ◽  
Consistency And Asymptotic Normality ◽  
Poisson Shot Noise

Stochastic processes {X(t)} of the form X(t) = Σ n f(t – Tn ) are considered, where {Tn } is a stationary Poisson point process with intensity λ and f: R → R is an unknown response function. Conditions are obtained for weak consistency and asymptotic normality of estimators of λ based on long-run observations of {X(t)}.

Some applications of weak convergence to statistics

1988 ◽  
Vol 25 (A) ◽  
pp. 201-211
Author(s):  
R. M. Loynes
Keyword(s):  
Weak Convergence ◽  
Stochastic Processes ◽  
Asymptotic Properties ◽  
Convergence Results

Results showing the weak convergence of certain stochastic processes are used to derive both known and new (asymptotic) properties of signs of residuals from regression; other weak convergence results are derived, and used to determine the behaviour of runs of residuals.

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