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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

1 vote

Law of large numbers for random functions?

The sequence $$ \{ h(X_1, \hat \theta_n), \ldots, h(X_n, \hat \theta_n) \} $$ is a row-wise exchangeable triangular array. This appears to be the result you need http://www.tandfonline.com/doi/pdf/1 …
izmirlig's user avatar
1 vote

Is there an Itō formula for random functions in infinite-dimensions?

The case when the drift and diffusion coefficients for $X$ are bounded is easy-- the following hand wavy proof is almost a proof. Because of the isometries between all seperable Hilbert spaces and the …
izmirlig's user avatar