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Hölder continuity for spatial and path processes via spectral analysis
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  • Published: March 2001

Hölder continuity for spatial and path processes via spectral analysis

  • Douglas Blount1 &
  • Michael A. Kouritzin2 

Probability Theory and Related Fields volume 119, pages 589–603 (2001)Cite this article

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  • 3 Citations

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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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Authors and Affiliations

  1. Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, USA. e-mail: blount@math.la.asu.edu, , , , , , US

    Douglas Blount

  2. Department of Mathematical Sciences, Universiy of Alberta, Edmonton, Alberta, Canada T6G 2G1. e-mail: mkouritz@math.ualberta.ca, , , , , , CA

    Michael A. Kouritzin

Authors
  1. Douglas Blount
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  2. Michael A. Kouritzin
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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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  • Issue Date: March 2001

  • DOI: https://doi.org/10.1007/PL00008773

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  • Mathematics Subject Classification (2000): Primary 60H15; Secondary 60G57, 60G17
  • Key words or phrases: Hölder continuity – Stochastic partial differential equations – Superprocesses – Path process – Fourier analysis
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