Displaying similar documents to “Two results on continuity and boundedness of stochastic convolutions”

Path-wise solutions of stochastic differential equations driven by Lévy processes.

David R. E. Williams (2001)

Revista Matemática Iberoamericana

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In this paper we show that a path-wise solution to the following integral equation Yt = ∫0 t  f(Yt) dXt,     Y0 = a ∈ Rd, exists under the assumption that Xt is a Lévy process of finite p-variation for some p ≥ 1 and that f is an α-Lipschitz function for some α >...

Strong law of large numbers for fragmentation processes

S. C. Harris, R. Knobloch, A. E. Kyprianou (2010)

Annales de l'I.H.P. Probabilités et statistiques

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In the spirit of a classical result for Crump–Mode–Jagers processes, we prove a strong law of large numbers for fragmentation processes. Specifically, for self-similar fragmentation processes, including homogenous processes, we prove the almost sure convergence of an empirical measure associated with the stopping line corresponding to first fragments of size strictly smaller than for 1≥>0.

Moments of some random functionals

K. Urbanik (1997)

Colloquium Mathematicum

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The paper deals with nonnegative stochastic processes X(t,ω)(t ≤ 0) not identically zero with stationary and independent increments right-continuous sample functions and fulfilling the initial condition X(0,ω)=0. The main aim is to study the moments of the random functionals ∫ 0 ∞ f ( X ( τ , ω ) ) d τ for a wide class of functions f. In particular a characterization of deterministic processes in terms of the exponential moments of these functionals is established.