On weak convergence to random processes with boundary conditions

1982 ◽  
pp. 260-275 ◽  
Author(s):  
B. Grigelionis ◽  
R. Mikulevicius
Keyword(s):  
Weak Convergence ◽  
Boundary Conditions ◽  
Random Processes

scholarly journals Brane webs and random processes

2015 ◽  
Vol 30 (33) ◽  
pp. 1550202 ◽  
Author(s):  
Amer Iqbal ◽  
Babar A. Qureshi ◽  
Khurram Shabbir ◽  
Muhammad A. Shehper
Keyword(s):  
Partition Function ◽  
Boundary Conditions ◽  
Generating Function ◽  
Random Processes ◽  
Open String ◽  
Plane Partitions ◽  
Schur Process ◽  
String Amplitudes

We study (p, q) 5-brane webs dual to certain N M5-brane configurations and show that the partition function of these brane webs gives rise to cylindric Schur process with period N. This generalizes the previously studied case of period 1. We also show that open string amplitudes corresponding to these brane webs are captured by the generating function of cylindric plane partitions with profile determined by the boundary conditions imposed on the open string amplitudes.

scholarly journals Weak Convergence for a Class of Stochastic Fractional Equations Driven by Fractional Noise

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Xichao Sun ◽  
Junfeng Liu
Keyword(s):  
Weak Convergence ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Dirichlet Boundary ◽  
Random Perturbation ◽  
Continuous Functions ◽  
Dirichlet Boundary Conditions ◽  
Fractional Noise ◽  
Fractional Heat Equation ◽  
Fractional Equations

We consider a class of stochastic fractional equations driven by fractional noise ont,x∈0,T×0,1  ∂u/∂t=Dδαu+ft,x,u+∂2BHt,x/∂t ∂x, with Dirichlet boundary conditions. We formally replace the random perturbation by a family of sequences based on Kac-Stroock processes in the plane, which approximate the fractional noise in some sense. Under some conditions, we show that the real-valued mild solution of the stochastic fractional heat equation perturbed by this family of noises converges in law, in the space𝒞0,T×0,1of continuous functions, to the solution of the stochastic fractional heat equation driven by fractional noise.

scholarly journals Weak convergence of random processes with immigration at random times

2020 ◽  
Vol 57 (1) ◽  
pp. 250-265
Author(s):  
Congzao Dong ◽  
Alexander Iksanov
Keyword(s):  
Weak Convergence ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Random Processes ◽  
Branching Random Walk ◽  
General Point ◽  
Shot Noise Process ◽  
Finite Dimensional ◽  
Strong Resemblance ◽  
Random Times

AbstractBy a random process with immigration at random times we mean a shot noise process with a random response function (response process) in which shots occur at arbitrary random times. Such random processes generalize random processes with immigration at the epochs of a renewal process which were introduced in Iksanov et al. (2017) and bear a strong resemblance to a random characteristic in general branching processes and the counting process in a fixed generation of a branching random walk generated by a general point process. We provide sufficient conditions which ensure weak convergence of finite-dimensional distributions of these processes to certain Gaussian processes. Our main result is specialised to several particular instances of random times and response processes.

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