Convergence in (2m)-th mean for perturbed stochastic integrodifferential equations
This paper deals with convergence model of interest rates, which explains the evolution of interest rate in connection with the adoption of Euro currency. Its dynamics is described by two stochastic differential equations – the domestic and the European short rate. Bond prices are then solutions to partial differential equations. For the special case with constant volatilities closed form solutions for bond prices are known. Substituting its constant volatilities by instantaneous volatilities we...
We discuss here several types of convergence of conditional expectations for unbounded closed convex random sets of the form where is a decreasing sequence of sub-σ-algebras and is a sequence of closed convex random sets in a separable Banach space.
We present a spectral theory for a class of operators satisfying a weak “Doeblin–Fortet” condition and apply it to a class of transition operators. This gives the convergence of the series , , under some regularity assumptions and implies the central limit theorem with a rate in for the corresponding Markov chain. An application to a non uniformly hyperbolic transformation on the interval is also given.
We present a spectral theory for a class of operators satisfying a weak “Doeblin–Fortet" condition and apply it to a class of transition operators. This gives the convergence of the series ∑k≥0krPkƒ, , under some regularity assumptions and implies the central limit theorem with a rate in for the corresponding Markov chain. An application to a non uniformly hyperbolic transformation on the interval is also given.