WELL-POSEDNESS OF STOCHASTIC NONLINEAR HEAT AND WAVE EQUATIONS DRIVEN BY SUBORDINATE CYLINDRICAL BROWNIAN NOISES ON THE TWO-DIMENSIONAL TORUS (Nonlinear and Random Waves)

[1] S. Albeverio, V. Mandrekar and B. Rudiger. Existence of mild solutions for stochastic differential equations and

semilinear equations with non-Gaussian Levy noise. Stochastic Process. Appl. 119 (2009), no. 3, 835-863.

[2] D. Applebaum. Levy processes and stochastic calculus. Cambridge Studies in Advanced Mathematics, 93. Cambridge University Press, Cambridge, 2004.

[3] Z. Brzezniak and J. Zabczyk. Regularity of Ornstein-Uhlenbeck processes driven by a Levy white noise. Potential

Anal., 32 (2010), 153-188.

[4] R. Catellier and K. Chouk. Paracontrolled distributions and the 3-dimensional stochastic quantization equation.

Ann. Probab. 46 (2018), no. 5, 2621-2679.

[5] G. Da Prato and A. Debussche. Strong solutions to the stochastic quantization equations. The Ann. Probab.

(2003), Vol. 31, No. 4, 1900-1916.

[6] Z. Dong, L. Xu and X. Zhang. Exponential ergodicity of stochastic Burgers equations driven by a-stable processes.

J. Stat. Phys. 154 (2014), no. 4, 929-949.

[7] M. Gubinelli, P. Imkeller and N. Perkowski. Paracontrolled distributions and singular PDEs. Forum Math. Pi 3

(2015), e6, 75 pp.

[8] M. Gubinelli, H. Koch and T. Oh. Renormalization of the two-dimensional stochastic nonlinear wave equations.

Trans. Amer. Math. Soc. (2018), Vol. 370, No. 10, 7335-7359.

[9] M. Gubinelli, H. Koch, T. Oh and L. Tolomeo. Global Dynamics for the Two-dimensional Stochastic Nonlinear

Wave Equations. International Mathematics Research Notices, rnab084, https://doi.org/10.1093/imrn/rnab084.

[10] M. Hairer. A theory of regularity structures. Invent. Math. 198 (2014), no. 2, 269-504.

[11] T. Meyer-Brandis and F. Proske. Explicit representation of strong solutions of SD Es driven by infinite dimensional

Levy processes. J. Theor. Prob., 23:301-314, 2010.

30

WELL-POSEDNESS OF SPDES DRIVEN BY SUBORDINATE CYLINDRICAL BROWNIAN NOISES

[12] H. Nagoji. Renormalization of stochastic nonlinear heat and wave equations driven by subordinate cylindrical

Brownian noises. arXiv:2201.08010 [math.PR]

[13] T. Oh and M. Okamoto. Comparing the stochastic nonlinear wave and heat equations: a case study. Electron. J.

Probab. 26 (2021), Paper No. 9, 44 pp.

[14] S. Peszat and J. Zabczyk. Stochastic partial differential equations with Levy noise. An evolution equation approach. Encyclopedia of Mathematics and its Applications, 113. Cambridge University Press, Cambridge, 2007.

xii+419 pp.

[15] E. Priola and J. Zabczyk. Structural properties of semilinear SPDEs driven by cylindrical stable processes.

Probab. Theory Related Fields 149 (2011), no. 1-2, 97-137.

[16] B. Rudiger and G. Ziglio. Ito formula for stochastic integrals w.r.t compensated Poisson random measures on

separable Banach spaces. Stochastics, 78:377-410, 2006.

[17] J. Wang and Y. Rao. A note on stability of SPDEs driven by a-stable noises. Adv. Difference Equ. 2014, 2014:98,

11 pp.

[18] J. H. Zhu and Z. Brzezniak. Nonlinear stochastic partial differential equations of hyperbolic type driven by

Levy-type noises. Discrete Contin. Dyn. Syst. Ser. B, 21 (2016), 3269-3299.

GRADUATE SCHOOL OF SCIENCE, KYOTO UNIVERSITY, KITASHIRAKAWA-OIWAKECHO, SAKYO-KU, KYOTO 6068502, JAPAN

Email address: nagoji .hirotatsu. 63x©st. kyoto-u. ac. jp

...