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Integral equations with respect to a general stochastic measure

Author: V. M. Radchenko
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 91 (2014).
Journal: Theor. Probability and Math. Statist. 91 (2015), 169-179
MSC (2010): Primary 60H20, 60H05, 60G57
Published electronically: February 4, 2016
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Abstract: An integral with respect to a general stochastic measure is defined for random functions whose trajectories belong to a Besov space. The existence and uniqueness of solutions of some stochastic equations involving such integrals are established.

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  • 1. S. Ogawa, Stochastic integral equations for the random fields, Seminaire de Probabilites XXV, Springer, Berlin-Heidelberg, 1991, pp. 324-329. MR 1187790 (94b:60073)
  • 2. T. Mikosch and R. Norvaiša, Stochastic integral equations without probability, Bernoulli 6 (2000), no. 3, 401-434. MR 1762553 (2001h:60100)
  • 3. V. M. Radchenko, Mild solution of the heat equation with a general stochastic measure, Studia Math. 194 (2009), no. 3, 231-251. MR 2539554 (2010j:60157)
  • 4. V. Radchenko, Stochastic partial differential equations driven by general stochastic measures, Modern Stochastics and Applications (V. Korolyuk, N. Limnios, Yu. Mishura, L. Sakhno, and G. Shevchenko, eds.), Springer/Cham Heidelberg, 2014, pp. 143-156. MR 3236073
  • 5. S. Kwapień and W. A. Woycziński, Random Series and Stochastic Integrals: Single and Multiple, Birkhäuser, Boston, 1992. MR 1167198 (94k:60074)
  • 6. J. Memin, Yu. Mishura, and E. Valkeila, Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion, Statist. Probab. Lett. 27 (2001), no. 2, 197-206. MR 1822771 (2002b:60096)
  • 7. G. Samorodnitsky and M. Taqqu, Stable Non-Gaussian Random Processes, Chapman and Hall, London, 1994. MR 1280932 (95f:60024)
  • 8. V. N. Radchenko, Integrals with respect to general random measures, Proceedings of Institute of Mathematics, National Academy of Science of Ukraine 27 (1999). (Russian)
  • 9. G. Curbera and O. Delgado, Optimal domains for $ {L}^0$-valued operators via stochastic measures, Positivity 11 (2007), no. 3, 399-416. MR 2336205 (2008g:46063)
  • 10. V. Radchenko, Besov regularity of stochastic measures, Statist. Probab. Lett. 77 (2007), no. 8, 822-825. MR 2369688 (2009c:60126)
  • 11. A. Kamont, A discrete characterization of Besov spaces, Approx. Theory Appl. (N.S.) 13 (1997), no. 2, 63-77. MR 1750304 (2001e:46058)
  • 12. V. N. Radchenko, On a definition of the integral of a random function, Teor. Veroyatnost. Primenen. 41 (1996), no. 3, 677-682; English transl. in Theory Probab. Appl. 41 (1997), no. 3, 597-601. MR 1450086 (98f:60002)

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Additional Information

V. M. Radchenko
Affiliation: Department of Mathematical Analysis, National Taras Shevchenko University, Kyiv 01601, Ukraine

Keywords: Stochastic measure, stochastic integral, stochastic differential equation, Besov space
Received by editor(s): August 29, 2014
Published electronically: February 4, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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