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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 7
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Research Article

On the small time asymptotics of scalar stochastic conservation laws

Zhao Donga RCSDS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China;b School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, ChinaView further author information
&
Rangrang Zhangc School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, ChinaCorrespondence[email protected]
View further author information
Pages 1889-1913 | Received 11 May 2021, Accepted 16 Nov 2021, Published online: 03 Dec 2021

References

  • Dafermos CM. Hyperbolic conservation laws in continuum physics. 2nd ed. Berlin: Springer; 2005.
  • Ammar K, Wittbold P, Carrillo J. Scalar conservation laws with general boundary condition and continuous flux function. J Differ Equ. 2006;228(1):111–139.
  • Kružkov SN. Generalized solutions of the Cauchy problem in the large for first order nonlinear equations. Dokl Akad Nauk SSSR. 1969;187:29–32.
  • Kružkov SN. First order quasilinear equations with several independent variables. Mat Sb (NS). 1970;81(123):228–255.
  • Lions PL, Perthame B, Tadmor E. A kinetic formulation of multidimensional scalar conservation laws and related equations. J AMS. 1994;7:169–191.
  • Kim JU. On a stochastic scalar conservation law. Indiana Univ Math J. 2003;52:227–256.
  • Vallet G, Wittbold P. On a stochastic first-order hyperbolic equation in a bounded domain. Infinite Dimens Anal Quantum Probab Relat Top. 2009;12(4):613–651.
  • Feng J, Nualart D. Stochastic scalar conservation laws. J Funct Anal. 2008;255(2):313–373.
  • Debussche A, Vovelle J. Scalar conservation laws with stochastic forcing (revised version). J Funct Anal. 2010;259(4):1014–1042.
  • Debussche A, Vovelle J. Invariant measure of scalar first-order conservation laws with stochastic forcing. Probab Theory Rel Fields. 2015;163(3–4):575–611.
  • Dong Z, Wu J-L, Zhang R, et al. Large derivation principles for first-order scalar conservation laws with stochastic forcing. Ann Appl Probab. 2020;30(1):324–367.
  • Varadhan SRS. Diffusion processes in a small time interval. Commun Pure Appl Math. 1967;20:659–685.
  • Aida S, Kawabi H. Short time asymptotics of a certain infinite dimensional diffusion process. In: Dereich S, Khoshnevisan D, Kyprianou AE, et al., editors. Stochastic analysis and related topics, VII (Kusadasi, 1998). Boston (MA): Birkhäuser Boston; 2001. p. 77–124 (Progr. Probab.; 48).
  • Aida S, Zhang T. On the small time asymptotics of diffusion processes on path groups. Potential Anal. 2002;16(1):67–78.
  • Fang S, Zhang T. On the small time behavior of Ornstein–Uhlenbeck processes with unbounded linear drifts. Probab Theory Relat Fields. 1999;114(4):487–504.
  • Hino M, Ramírez J. Small-time Gaussian behavior of symmetric diffusion semigroups. Ann Probab. 2003;31(3):1254–1295.
  • Zhang T. On the small time asymptotics of diffusion processes on Hilbert spaces. Ann Probab. 2000;28(2):537–557.
  • Xu T, Zhang T. On the small time asymptotics of the two-dimensional stochastic Navier–Stokes equations. Ann Inst Henri Poincaré Probab Stat. 2009;45(4):1002–1019.
  • Dong Z, Zhang R. On the small time asymptotics of 3D stochastic primitive equations. Math Methods Appl Sci. 2018;41(16):6336–6357.
  • Debussche A, Hofmanová M, Vovelle J. Degenerate parabolic stochastic partial differential equations: quasilinear case. Ann Probab. 2016;44(3):1916–1955.
  • Dembo A, Zeitouni O. Large deviations techniques and applications. Boston (MA): Jones and Bartlett; 1993.
  • Revuz D, Yor M. Continuous martingales and Brownian motion. Berlin: Springer-Verlag; 1999 (Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 293).
  • Barlow MT, Yor M. Semi-martingale inequalities via the Garsia–Rodemich–Rumsey lemma and applications to local time. J Funct Anal. 1982;49:198–229.
  • Davis B. On the Lp norms of stochastic integrals and other martingales. Duke Math J. 1976;43:697–704.

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