The Central Limit Theorem for Stochastic Integrals with Respect to Levy Processes

On the Central Limit Theorem for Multiparameter Stochastic Processes

l.INTRODUCTION AND RESULTS In recent papers Bezandry and Fernique (1990,1992), Fernique (1993) have given new convergence and tightness criteria for random processes whose sample paths are right-continuous and have leftlimits. These criteria have been applied by Bezandry and Fernique, Bloznelis and Paulauskas to prove the central limit theorem (CLT) in the Skorohod space D[0, 1]. In this paper,...

Set-Valued Stochastic Integrals with Respect to Finite Variation Processes

In a Euclidean space , the Lebesgue-Stieltjes integral of set-valued stochastic processes d R       , 0, t F F t T    with respect to real valued finite variation process       , 0, t A t T   t is defined directly by employing all integrably bounded selections instead of taking the decomposable closure appearing in some existed references. We shall show that this kind of integr...

Central Limit Theorem for Stationary Linear Processes

We establish the central limit theorem for linear processes with dependent innovations including martingales and mixingale type of assumptions as defined in McLeish [Ann. In doing so we shall preserve the generality of the coefficients, including the long range dependence case, and we shall express the variance of partial sums in a form easy to apply. Ergodicity is not required.

Central Limit Theorem for Nonlinear Hawkes Processes

Hawkes process is a self-exciting point process with clustering effect whose jump rate depends on its entire past history. It has wide applications in neuroscience, finance and many other fields. Linear Hawkes process has an immigration-birth representation and can be computed more or less explicitly. It has been extensively studied in the past and the limit theorems are well understood. On the...

A Probability Bound for Integrals with Respect to Stochastic Processes with Independent Increments1