We analyse analytic properties of nonlocal transition semigroups associated with a class of stochastic differential equations (SDEs) in R^d driven by pure jump–type Lévy processes. First, we will show under which conditions the semigroup will be analytic on the Besov space B^m_
[1] H. Abels: Pseudo-differential and singular integral operators, An introduction with applications, De Gruyter Graduate Lectures, De Gruyter, Berlin, 2012.
[2] D. Applebaum: Le´vy processes and stochastic calculus, 2nd edition, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 2009.
[3] S. Asmussen and J. Rosin´ski: Approximations of small jumps of Le´vy processes with a view towards simu- lation, J. App. Prob. 38 (2001), 482–493.
[4] H. Bahouri, J.Y. Chemin and R. Danchin: Fourier analysis and nonlinear partial differential equations, A series of comprehensive studies in Mathematics, Springer-Verlag, Berlin, 2011.
[5] V. Bally, D. Goreac and V. Rabiet: Regularity and stability for the semigroup of jump diffusions with state- dependent intensity, Ann. Appl. Probab. 28 (2018), 3028–3074.
[6] O.E. Barndorff-Nielsen: Processes of normal inverse Gaussian type, Finance Stoch 2 (1998), 41–68.
[7] R.M. Blumenthal and R.K. Getoor: Sample functions of stochastic processes with stationary independent increments, J. Math. Mech. 10 (1961), 493–516.
[8] B. Bo¨ttcher and N. Jacob: Remarks on Meixner-type processes; in Probabilistic methods in fluids, World Sci. Publ., River Edge, NJ, 2003, 35–47.
[9] B. Bo¨ttcher, R. Schilling and J. Wang: Le´vy matters III, Le´vy-type processes: construction, approximation and sample path properties, Le´vy matters, Springer International Publishing Switzerland, 2013.
[10] Z. Brze´zniak, E. Hausenblas and P.A. Razafimandimby: Stochastic reaction-diffusion equations driven by jump processes, Potential Anal. 49 (2017), 131–201.
[11] S. Cox and E. Hausenblas: A perturbation result for semi-linear stochastic differential equations in UMD Banach spaces, J. Evol. Equ. 13 (2013), 795–827.
[12] Z. Dong, S. Peszat and L. Xu: On some smoothening effects of the transition semigroup of a Le´vy process, J. Math. Anal. Appl. 434 (2016), 1566–1580.
[13] K. Engel and R. Nagel: One-parameter semigroups for linear evolution equations, Graduate Texts in Math- ematics, Springer-Verlag, New York, 2000.
[14] B.P.W. Fernando and E. Hausenblas: Nonlinear filtering with correlated Le´vy noise characterized by cop- ulas, Braz. J. Probab. Stat. 32 (2018), 374–421.
[15] B. Fernando, E. Hausenblas and P. Razafimandimby: Analytic properties of markov semigroup generated by stochastic differential equations driven by Le´vy processes, Potential Anal. 46 (2017), 1–21.
[16] K. Glau: Sobolev index: a classification of Le´vy processes via their symbols, arXiv:1203.0866, 2012.
[17] A. Gomilko and Y. Tomilov: On subordination of holomorphic semigroups, Adv. Math. 283 (2015), 155– 194.
[18] M. Haase: The functional calculus for sectorial operators, Operator Theory: Advances and Applications 169, Birkha¨user Verlag, Basel, 2006.
[19] E. Hausenblas: Approximation for semilinear stochastic evolution equations, Potential Anal. 18 (2003), 141–186.
[20] W. Hoh: A symbolic calculus for pseudo-differential operators generating feller semigroups, Osaka J. Math. 35 (1998), 789–820.
[21] L. Ho¨rmander: Estimates for translation invariant operators in Lp spaces, Acta Math. 104 (1960), 93–140.
[22] Y. Ishikawa: Stochastic calculus of variations for jump processes, De Gruyter, Berlin, Boston, 2013.
[23] Y. Ishikawa, H. Kunita and M. Tsuchiya: Smooth density and its short time estimate for jump process determined by SDE, Stochastic Process. Appl. 128 (2018), 3181–3219.
[24] N. Jacob: Pseudo differential operators and Markov processes vol. I, Fourier analysis and semigroups, Imperial College Press, London, 2000.
[25] N. Jacob: Pseudo differential operators and Markov processes vol. II, Generators and their potential theory, Imperial College Press, London, 2002.
[26] N. Jacob: Pseudo differential operators and Markov processes vol. III, Markov processes and applications, Imperial College Press, London, 2005.
[27] D. Khoshnevisan and R.L. Schilling: From Le´vy-type processes to parabolic SPDEs, Advanced Courses in Mathematics - CRM Barcelona, Birkha¨user Basel, Springer International Publishing Switzerland, 2016.
[28] P. Kim, R. Song and Z. Vondracek: Heat kernels of non-symmetric jump processes: Beyond the stable case. Potential Anal. 49 (2017), 1–54.
[29] V.N. Kolokoltsov: On Markov processes with decomposable pseudo-differential generators, Stoch. Stoch. Rep. 76 (2004), 1–44.
[30] H. Kumana-Go: Pseudo-differential operators, MIT Press, Cambridge, 1982.
[31] S. Kusuoka and C. Marinelli: On smoothing properties of transition semigroups associated to a class of SDEs with jumps, Ann. Inst. Henri Poincare´ Probab. Stat. 50 (2014), 1347–1370.
[32] U. Ku¨chler and S. Tappe: Tempered stable distributions and processes, Stochastic Process. Appl. 123 (2013), 4256–4293.
[33] F. Ku¨hn: Solutions of Le´vy-driven SDEs with unbounded coeflcients as feller processes, Proc. Amer. Math. Soc. 146 (2018), 3591–3604.
[34] F. Nicola and L. Rodino: Global pseudo-differential calculus on Euclidean spaces, Pseudo-differential operators, Modern Birkha¨user Classics vol. 4, Birkha¨user Verlag, Basel, 2010.
[35] A. Pazy: Semigroups of linear operators and applications to partial differential equations, Applied Mathe- matical Sciences 44, Springer-Verlag, New York, 1983.
[36] J. Picard: Density in small time at accessible points for jump processes, Stochastic Process. Appl. 67 (1997), 251–279.
[37] C. Rama and P. Peter: Financial modelling with jump processes, Financial Mathematics Series, FL Chap- man and Hall/CRC, Boca Raton, 2003.
[38] T. Runst and W. Sickel: Sobolev spaces of fractional order, Nemytskij operators, and nonlinear partial differential equations, De Gruyter series in nonlinear analysis and applications 3, Walter de Gruyter, Berlin, Germany, 1996.
[39] K. Sato: Le´vy processes and infinitely divisible distributions, Cambridge Studies in Advanced Mathematics 68, Cambridge University Press, Cambridge, 1999.
[40] R. Schilling: On Feller processes with sample paths in Besov spaces, Math. Ann. 309 (1997), 663–675.
[41] R. Schilling: Growth and Ho¨lder conditions for the sample paths of Feller processes, Probab. Theory Related Fields 112 (1998), 565–611.
[42] R. Schilling: From Le´vy-type processes to parabolic SPDEs, Advanced Courses in Mathematics - CRM Barcelona, Birkha¨user Basel, Springer International Publishing Switzerland, 2016.
[43] R. Schilling and A. Schnurr: The symbol associated with the solution of a stochastic differential equation, Electron. J. Probab. 15 (2010), 1369–1393.
全国の大学の
卒論・修論・学位論文
を
一発検索！
論文の公開元へ