Abstract.
For ν(dθ), a σ-finite Borel measure on R d, we consider L 2(ν(dθ))-valued stochastic processes Y(t) with te property that Y(t)=y(t,·) where y(t,θ)=∫t 0 e −λ(θ)( t − s ) dm(s,θ) and m(t,θ) is a continuous martingale with quadratic variation [m](t)=∫t 0 g(s,θ)ds. We prove timewise Hölder continuity and maximal inequalities for Y and use these results to obtain Hilbert space regularity for a class of superrocesses as well as a class of stochastic evolutions of the form dX=AXdt+GdW with W a cylindrical Brownian motion. Maximal inequalities and Hölder continuity results are also provenfor the path process t (τ)≗Y(τt∧t).
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Received: 25 June 1999 / Revised version: 28 August 2000 /¶Published online: 9 March 2001
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Blount, D., Kouritzin, M. Hölder continuity for spatial and path processes via spectral analysis. Probab Theory Relat Fields 119, 589–603 (2001). https://doi.org/10.1007/PL00008773
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DOI: https://doi.org/10.1007/PL00008773
- Mathematics Subject Classification (2000): Primary 60H15; Secondary 60G57, 60G17
- Key words or phrases: Hölder continuity – Stochastic partial differential equations – Superprocesses – Path process – Fourier analysis