Heat equation and wave equation with general stochastic measures
- V. N. Radchenko
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We consider the heat equation and wave equation with constant coefficients that contain a term given by an integral with respect to a random measure. Only the condition of sigma-additivity in probability is imposed on the random measure. Solutions of these equations are presented. For each equation, we prove that its solutions coincide under certain additional conditions.
- V. I. Klyatskin, Stochastic Equations through the Eye of the Physicist [in Russian], Fizmatlit, Moscow (2001).
- A. Sturm, “On convergence of population processes in random environments to the stochastic heat equation with colored noise,” Electron. J. Probab., 8, No. 6, 1–39 (2003).
- I. M. Gel’fand and N. Ya. Vilenkin, Generalized Functions, Vol. 4, Some Application of Harmonic Analysis. Rigged Hilbert Spaces [in Russian], Fizmatgiz, Moscow (1961).
- E. Pardoux, “Stochastic partial differential equations. A review,” Bull. Sci. Math., Sér. 2 e , 117, 29–47 (1993).
- B. L. Rozovskii, Evolution Stochastic Systems [in Russian], Nauka, Moscow (1983).
- K.-H. Kim, “Stochastic partial differential equations with variable coefficients in C 1 domains,” Stochast. Process. Appl., 112, 261–283 (2004). CrossRef
- J. B. Walsh, “An introduction to stochastic partial differential equations,” Lect. Notes Math., 1180, 236–434 (1984).
- R. C. Dalang, “Extending martingale measure stochastic integral with applications to spatially homogeneous SPDE’s,” Electron. J. Probab., 4, No. 6, 1–29 (1999).
- R. C. Dalang and C. Mueller, “Some non-linear SPDE’s that are second order in time,” Electron. J. Probab., 8, No. 1, 1–21 (2003).
- D. Conus and R. C. Dalang, “The non-linear stochastic wave equation in high dimensions,” Electron. J. Probab., 13, No. 22, 629–670 (2008).
- H. Holden, B. Óksendal, L. Ubóe, and T. Zhang, Stochastic Partial Differential Equations. A Modelling White Noise Functional Approach, Birkhäuser, Boston (1996).
- Yu. A. Rozanov, Random Fields and Stochastic Partial Differential Equations [in Russian], Fizmatlit, Moscow (1995).
- J. Memin, Yu. Mishura, and E. Valkeila, “Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion,” Statist. Probab. Lett., 51, 197–206 (2001). CrossRef
- S. Kwapień and W. A. Woycziński, Random Series and Stochastic Integrals: Single and Multiple, Birkhäuser, Boston (1992).
- V. N. Radchenko, Integrals with Respect to General Random Measures [in Russian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev (1999).
- V. N. Radchenko, “Integrals with respect to random measures and random linear functionals,” Teor. Ver. Primen., 36, No. 3, 594–596 (1991).
- V. S. Vladimirov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1971).
- A. A. Kirillov and A. D. Gvishiani, Theorems and Problems of Functional Analysis [in Russian], Nauka, Moscow (1979).
- K. Yosida, Functional Analysis, Springer, Berlin (1965).
- V. N. Radchenko, “On convergence of integrals with respect to L 0-valued measures,” Mat. Zametki, 53, No. 5, 102–106 (1993).
- Heat equation and wave equation with general stochastic measures
Ukrainian Mathematical Journal
Volume 60, Issue 12 , pp 1968-1981
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- V. N. Radchenko (1)
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- 1. Shevchenko Kyiv National University, Kyiv, Ukraine