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5 papers · 2 filters
A functional central limit theorem for a class of urn models
Gopal K Basak, Amites Dasgupta
We construct an independent increments Gaussian process associated to a class of multicolor urn models. The construction uses random variables from the urn model which are differen…
Central limit theorems for a class of irreducible multicolor urn models
Gopal K. Basak, Amites Dasgupta
We take a unified approach to central limit theorems for a class of irreducible urn models with constant replacement matrix. Depending on the eigenvalue, we consider appropriate li…
Rigorous results on the threshold network model
Norio Konno, Naoki Masuda, Rahul Roy +1
We analyze the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some…
Infinite dimensional stochastic differential equations of Ornstein-Uhlenbeck type
Siva R. Athreya, Richard F. Bass, Maria Gordina +1
We consider the operator $$\sL f(x)=\tfrac12 \sum_{i,j=1}^\infty a_{ij}(x)\frac{\del^2 f}{\del x_i \del x_j}(x)-\sum_{i=1}^\infty \lam_i x_i b_i(x) \frac{\del f}{\del x_i}(x).$$ We…
Measure free martingales
Rajeeva L Karandikar, M G Nadkarni
We give a necessary and sufficient condition on a sequence of functions on a set under which there is a measure on which renders the given sequence of functions a martingal…