The mean square convergence of PPDA projection index

2008 ◽  
Author(s):  
Zhigang Zhang ◽  
Junqing Tian ◽  
Ying Ren
Keyword(s):  
Mean Square ◽  
Projection Index ◽  
Mean Square Convergence ◽  
The Mean

Asymptotic behaviour of immigration-branching processes by general set of types. II: Supercritical branching part

1975 ◽  
Vol 7 (03) ◽  
pp. 468-494
Author(s):  
H. Hering
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Almost Sure Convergence ◽  
Transition Function ◽  
Mean Square ◽  
Second Moments ◽  
Mean Square Convergence ◽  
The Mean ◽  
Parameter Dependent ◽  
Dependent Probability

We construct an immigration-branching process from an inhomogeneous Poisson process, a parameter-dependent probability distribution of populations and a Markov branching process with homogeneous transition function. The set of types is arbitrary, and the parameter is allowed to be discrete or continuous. Assuming a supercritical branching part with primitive first moments and finite second moments, we prove propositions on the mean square convergence and the almost sure convergence of normalized averaging processes associated with the immigration-branching process.

Strong Convergence Analysis of Split-Step θ-Scheme for Nonlinear Stochastic Differential Equations with Jumps

2016 ◽  
Vol 8 (6) ◽  
pp. 1004-1022 ◽  
Author(s):  
Xu Yang ◽  
Weidong Zhao
Keyword(s):  
Differential Equations ◽  
Theoretical Result ◽  
Strong Convergence ◽  
Stochastic Differential Equations ◽  
Rate Of Convergence ◽  
Numerical Experiments ◽  
Mean Square ◽  
Nonlinear Stochastic Differential Equations ◽  
Mean Square Convergence ◽  
The Mean

AbstractIn this paper, we investigate the mean-square convergence of the split-step θ-scheme for nonlinear stochastic differential equations with jumps. Under some standard assumptions, we rigorously prove that the strong rate of convergence of the split-step θ-scheme in strong sense is one half. Some numerical experiments are carried out to assert our theoretical result.

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.

scholarly journals Convergence Rate of Numerical Solutions for Nonlinear Stochastic Pantograph Equations with Markovian Switching and Jumps

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Zhenyu Lu ◽  
Tingya Yang ◽  
Yanhan Hu ◽  
Junhao Hu
Keyword(s):  
Brownian Motion ◽  
Convergence Rate ◽  
Existence And Uniqueness ◽  
Numerical Solutions ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Mean Square ◽  
Mean Square Convergence ◽  
The Mean ◽  
Strong Order

The sufficient conditions of existence and uniqueness of the solutions for nonlinear stochastic pantograph equations with Markovian switching and jumps are given. It is proved that Euler-Maruyama scheme for nonlinear stochastic pantograph equations with Markovian switching and Brownian motion is of convergence with strong order 1/2. For nonlinear stochastic pantograph equations with Markovian switching and pure jumps, it is best to use the mean-square convergence, and the order of mean-square convergence is close to 1/2.

The convergence of a position-dependent branching process used as an approximation to a model describing the spread of an epidemic

1976 ◽  
Vol 13 (2) ◽  
pp. 338-344 ◽  
Author(s):  
J. Radcliffe
Keyword(s):  
Branching Process ◽  
Random Variable ◽  
Mean Square ◽  
Malthusian Parameter ◽  
Markov Branching Process ◽  
Geographical Spread ◽  
Mean Square Convergence ◽  
Velocity Of Propagation ◽  
The Mean ◽  
Number Of Individuals

A supercritical position-dependent Markov branching process has been used as an approximation to a model describing the initial geographical spread of a measles epidemic (Bartlett (1956)). Let α be its Malthusian parameter, ß its velocity of propagation, Z(A, t) the number of individuals in the set A at time t, and A√(ßt) = [√(ßt) r: r ∈ A]. The mean square convergence of the random variable W(A, t)= e–αtZ(A√(ßt), t) to a limit variable W(A) is established.

scholarly journals Mean-Square Convergence of Drift-Implicit One-Step Methods for Neutral Stochastic Delay Differential Equations with Jump Diffusion

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Lin Hu ◽  
Siqing Gan
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Mean Square ◽  
Stochastic Delay Differential Equations ◽  
Implicit Methods ◽  
Stochastic Delay ◽  
Mean Square Convergence ◽  
One Step ◽  
The Mean ◽  
Delay Differential

A class of drift-implicit one-step schemes are proposed for the neutral stochastic delay differential equations (NSDDEs) driven by Poisson processes. A general framework for mean-square convergence of the methods is provided. It is shown that under certain conditions global error estimates for a method can be inferred from estimates on its local error. The applicability of the mean-square convergence theory is illustrated by the stochastic θ-methods and the balanced implicit methods. It is derived from Theorem 3.1 that the order of the mean-square convergence of both of them for NSDDEs with jumps is 1/2. Numerical experiments illustrate the theoretical results. It is worth noting that the results of mean-square convergence of the stochastic θ-methods and the balanced implicit methods are also new.

scholarly journals The StochasticΘ-Method for Nonlinear Stochastic Volterra Integro-Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Peng Hu ◽  
Chengming Huang
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Numerical Experiments ◽  
Sufficient Condition ◽  
Asymptotically Stable ◽  
Mean Square ◽  
True Solution ◽  
Mean Square Exponential Stability ◽  
Mean Square Convergence ◽  
The Mean

The stochasticΘ-method is extended to solve nonlinear stochastic Volterra integro-differential equations. The mean-square convergence and asymptotic stability of the method are studied. First, we prove that the stochasticΘ-method is convergent of order1/2in mean-square sense for such equations. Then, a sufficient condition for mean-square exponential stability of the true solution is given. Under this condition, it is shown that the stochasticΘ-method is mean-square asymptotically stable for every stepsize if1/2≤θ≤1and when0≤θ<1/2, the stochasticΘ-method is mean-square asymptotically stable for some small stepsizes. Finally, we validate our conclusions by numerical experiments.

scholarly journals Superoptimal Rate of Convergence in Nonparametric Estimation for Functional Valued Processes

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Christophe Chesneau ◽  
Bertrand Maillot
Keyword(s):  
Rate Of Convergence ◽  
Nonparametric Estimation ◽  
Continuous Time ◽  
Regression Function ◽  
Mean Square ◽  
Semimetric Space ◽  
Mean Square Convergence ◽  
The Mean ◽  
Continuous Time Processes

We consider the nonparametric estimation of the generalised regression function for continuous time processes with irregular paths when the regressor takes values in a semimetric space. We establish the mean-square convergence of our estimator with the same superoptimal rate as when the regressor is real valued.

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