scholarly journals Convergence Analysis of Semi-Implicit Euler Methods for Solving Stochastic Age-Dependent Capital System with Variable Delays and Random Jump Magnitudes

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Qinghui Du ◽  
Chaoli Wang
Keyword(s):  
Convergence Analysis ◽  
Analytical Solutions ◽  
Numerical Approximation ◽  
Approximate Solutions ◽  
Mean Square ◽  
Variable Delays ◽  
Age Dependent ◽  
The Mean ◽  
Euler Methods ◽  
Random Jump

We consider semi-implicit Euler methods for stochastic age-dependent capital system with variable delays and random jump magnitudes, and investigate the convergence of the numerical approximation. It is proved that the numerical approximate solutions converge to the analytical solutions in the mean-square sense under given conditions.

scholarly journals A Compensated Numerical Method for Solving Stochastic Differential Equations with Variable Delays and Random Jump Magnitudes

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Ying Du ◽  
Changlin Mei
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Method ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Mean Square ◽  
Variable Delays ◽  
Mean Square Stability ◽  
The Mean ◽  
Random Jump

Stochastic differential equations with jumps are of a wide application area especially in mathematical finance. In general, it is hard to obtain their analytical solutions and the construction of some numerical solutions with good performance is therefore an important task in practice. In this study, a compensated split-stepθmethod is proposed to numerically solve the stochastic differential equations with variable delays and random jump magnitudes. It is proved that the numerical solutions converge to the analytical solutions in mean-square with the approximate rate of 1/2. Furthermore, the mean-square stability of the exact solutions and the numerical solutions are investigated via a linear test equation and the results show that the proposed numerical method shares both the mean-square stability and the so-called A-stability.

scholarly journals Convergence Analysis for the SMC-MeMBer and SMC-CBMeMBer Filters

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Feng Lian ◽  
Chen Li ◽  
Chongzhao Han ◽  
Hui Chen
Keyword(s):  
Monte Carlo ◽  
Convergence Analysis ◽  
Sequential Monte Carlo ◽  
Mean Square ◽  
Convergence Results ◽  
Mean Square Convergence ◽  
The Mean ◽  
Mean Square Errors

The convergence for the sequential Monte Carlo (SMC) implementations of the multitarget multi-Bernoulli (MeMBer) filter and cardinality-balanced MeMBer (CBMeMBer) filters is studied here. This paper proves that the SMC-MeMBer and SMC-CBMeMBer filters, respectively, converge to the true MeMBer and CBMeMBer filters in the mean-square sense and the corresponding bounds for the mean-square errors are given. The significance of this paper is in theory to present the convergence results of the SMC-MeMBer and SMC-CBMeMBer filters and the conditions under which the two filters satisfy mean-square convergence.

An age dependent branching process with variable lifetime distribution: The generation size

1974 ◽  
Vol 6 (02) ◽  
pp. 291-308 ◽  
Author(s):  
Robert Fildes
Keyword(s):  
Branching Process ◽  
Random Variable ◽  
Lifetime Distribution ◽  
Mean Square ◽  
Initial Particle ◽  
Age Dependent ◽  
The Mean ◽  
Watson Process ◽  
Number Of Particles

In a branching process with variable lifetime, introduced by Fildes (1972) define Yjk (t) as the number of particles alive in generation k at time t when the initial particle is born in generation j. A limit law similar to that derived in the Bellman-Harris process is proved where it is shown that Yjk (t) suitably normalised converges in mean square to a random variable which is the limit random variable of Znm–n in the Galton-Watson process (m is the mean number of particles born).

An age dependent branching process with variable lifetime distribution: The generation size

1974 ◽  
Vol 6 (2) ◽  
pp. 291-308 ◽  
Author(s):  
Robert Fildes
Keyword(s):  
Branching Process ◽  
Random Variable ◽  
Lifetime Distribution ◽  
Mean Square ◽  
Initial Particle ◽  
Age Dependent ◽  
The Mean ◽  
Watson Process ◽  
Number Of Particles

In a branching process with variable lifetime, introduced by Fildes (1972) define Yjk(t) as the number of particles alive in generation k at time t when the initial particle is born in generation j. A limit law similar to that derived in the Bellman-Harris process is proved where it is shown that Yjk(t) suitably normalised converges in mean square to a random variable which is the limit random variable of Znm–n in the Galton-Watson process (m is the mean number of particles born).

STABILITY OF HALF-LINEAR NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH DELAYS

2009 ◽  
Vol 80 (3) ◽  
pp. 369-383 ◽  
Author(s):  
MENG WU ◽  
NAN-JING HUANG ◽  
CHANG-WEN ZHAO
Keyword(s):  
Fixed Point Theory ◽  
Point Theory ◽  
Stability Theorem ◽  
Sufficient Condition ◽  
Mean Square ◽  
Necessary And Sufficient Condition ◽  
Variable Delays ◽  
Mean Square Stability ◽  
The Mean ◽  
Necessary And Sufficient

AbstractIn this paper, we study the mean square asymptotic stability of a generalized half-linear neutral stochastic differential equation with variable delays applying fixed point theory. An asymptotic mean square stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some results due to Burton, Zhang and Luo. Two examples are given to illustrate our results.

The asymptotic frequencies of the types in a multitype age-dependent branching process allowing immigration

1973 ◽  
Vol 10 (03) ◽  
pp. 652-658
Author(s):  
J. Radcliffe
Keyword(s):  
Renewal Process ◽  
Branching Process ◽  
Almost Sure Convergence ◽  
Mean Square ◽  
Malthusian Parameter ◽  
Age Dependent ◽  
The Mean

The mean square and almost sure convergence of W(t) = e–αt Z(t) is proved for a super-critical multitype age-dependent branching process allowing immigration at the epochs of a renewal process. It is shown that the Malthusian parameter, asymptotic frequencies of types and stationary age distributions are the same for the processes with and without immigration.

JUMP SYSTEMS WITH THE MEAN-REVERTING γ-PROCESS AND CONVERGENCE OF THE NUMERICAL APPROXIMATION

2012 ◽  
Vol 12 (02) ◽  
pp. 1150018 ◽  
Author(s):  
FENG JIANG ◽  
YI SHEN ◽  
FUKE WU
Keyword(s):  
Numerical Approximation ◽  
Option Price ◽  
Approximate Solutions ◽  
Analytical Properties ◽  
The Mean ◽  
Path Dependent ◽  
Jump Systems

In this paper, a class of jump systems with the mean-reverting γ-process are considered in finance. The analytical properties including the positivity, boundedness and pathwise estimations of the solution are discussed. Moreover, the authors show that the Euler–Maruyama approximate solutions converge to the true solutions in probability. Finally, the authors apply the convergence to examine a bond and a path-dependent option price in the financial pricing.

The asymptotic frequencies of the types in a multitype age-dependent branching process allowing immigration

1973 ◽  
Vol 10 (3) ◽  
pp. 652-658 ◽  
Author(s):  
J. Radcliffe
Keyword(s):  
Renewal Process ◽  
Branching Process ◽  
Almost Sure Convergence ◽  
Mean Square ◽  
Malthusian Parameter ◽  
Age Dependent ◽  
The Mean

The mean square and almost sure convergence of W(t) = e–αtZ(t) is proved for a super-critical multitype age-dependent branching process allowing immigration at the epochs of a renewal process. It is shown that the Malthusian parameter, asymptotic frequencies of types and stationary age distributions are the same for the processes with and without immigration.

The Bordeaux Automatic Meridian Circle

1978 ◽  
Vol 48 ◽  
pp. 227-228
Author(s):  
Y. Requième
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Meridian Circle ◽  
The Mean ◽  
Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

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