Uniform convergence in some limit theorems for multiple particle systems

Uniform Convergence in some Limit Theorems for Multiple Particle Systems

For n particles di using throughout R or Rd let n t A A B t be the random measure that counts the number of particles in A at time t It is shown that for some basic models Brownian particles with or without branching and di usion with a simple interaction the processes f n t E n t p n t M C L R g n N converge in law uniformly in t Previous results consider only convergence in law uniform in t b...

Uniform Convergence in some Limit Theoremsfor Multiple

For n particles diiusing throughout R (or R d), let n;t (A), A 2 B, t 0, be the random measure that counts the number of particles in A at time t. It is shown that for some basic models (Brownian particles with or without branching and diiusion with a simple interaction) the processes f(n;t () ? E n;t ())= p n : t 2 0; M]; 2 C L (R)g, n 2 N, converge in law uniformly in (t;). Previous results c...

Some Limit Theorems

Moment Convergence in Conditional Limit Theorems

SVANTE JANSON Abstract. Consider a sum ∑N 1 Yi of random variables conditioned on a given value of the sum ∑N 1 Xi of some other variables, where Xi and Yi are dependent but the pairs (Xi, Yi) form an i.i.d. sequence. We consider here the case when each Xi is discrete. We prove, for a triangular array ((Xni, Yni)) of such pairs satisfying certain conditions, both convergence of the distribution...

Moment Convergence in Conditional Limit Theorems

Consider a sum P N 1 Y i of random variables conditioned on a given value of the sum P N 1 X i of some other variables, where X i and Y i are dependent but the pairs (X i ; Y i) form an i.i.d. sequence. We prove, for a triangular array (X ni ; Y ni) of such pairs satisfying certain conditions, both convergence of the distribution of the conditioned sum (after suitable normalization) to a normal...