Cowpertwait, P., O'Connell, P., Metcalfe, A., and Mawdsley, J.: Stochastic
point process modelling of rainfall. I. Single-site fitting and validation,
J. Hydrol., 175, 17–46, 1996. a
Cox, D. R.: Renewal theory, Methuen, London, ISBN 978-0412205705, 1962. a
Deluca, A., Moloney, N. R., and Corral, Á.: Data-driven prediction of
thresholded time series of rainfall and self-organized criticality models,
Phys. Rev. E, 91, 052808,
https://doi.org/10.1103/PhysRevE.91.052808, 2015.
a
Evans, M. R., Majumdar, S. N., and Schehr, G.: Stochastic resetting and
applications, J. Phys. A., 53,
193001,
https://doi.org/10.1088/1751-8121/ab7cfe, 2020.
a
Filippov, A. F.: Differential equations with discontinuous righthand sides:
control systems, vol. 18, Springer Science & Business Media, ISBN 9789027726995, 2013. a
Gardiner, C. W.: Handbook of stochastic methods: for physics, chemistry & the
natural sciences, vol. 13 of Springer Series in Synergetics,
Springer–Verlag, Berlin, ISBN 9783540707127, 2004.
a,
b,
c
Green, J. R.: A model for rainfall occurrence, J. Roy. Stat. Soc. Ser. B,
26, 345–353, 1964. a
Hernandez-Duenas, G., Smith, L. M., and Stechmann, S. N.: Weak-and
strong-friction limits of parcel models: Comparisons and stochastic
convective initiation time, Q. J. Roy. Meteor. Soc., 145, 2272–2291,
https://doi.org/10.1002/qj.3557, 2019.
a
Hoeffding, W.: Probability inequalities for sums of bounded random variables,
in: The Collected Works of Wassily Hoeffding, Springer, 409–426, ISBN 9780387943107, 1994. a
Hottovy, S. A. and Stechmann, S. N.: A spatiotemporal stochastic model for
tropical precipitation and water vapor dynamics, J. Atmos. Sci., 72,
4721–4738,
https://doi.org/10.1175/JAS-D-15-0119.1, 2015a.
a,
b
Hottovy, S. A. and Stechmann, S. N.: Threshold models for rainfall and
convection: Deterministic versus stochastic triggers, SIAM J. Appl. Math.,
75, 861–884,
https://doi.org/10.1137/140980788, 2015b.
a,
b,
c,
d,
e
Katz, R. W.: Precipitation as a chain-dependent process, J. Appl.
Meteorol., 16, 671–676, 1977. a
Kelley, J. L.: General topology, Courier Dover Publications, ISBN 9783540901259, 2017.
a,
b
Khouider, B. and Majda, A. J.: A non-oscillatory balanced scheme for an
idealized tropical climate model: Part I: Algorithm and validation,
Theor. Comp. Fluid Dyn., 19, 331–354, 2005. a
Kurtz, T. G.: Random time changes and convergence in distribution under the
Meyer-Zheng conditions, Ann. Probab., 19, 1010–1034, 1991. a
Lejay, A. and Pigato, P.: A threshold model for local volatility: evidence of
leverage and mean reversion effects on historical data, Int. J.
Theor. Appl. Finan., 22, 1950017,
https://doi.org/10.1142/S0219024919500171, 2019.
a
Lin, J. and Neelin, J.: Influence of a stochastic moist convective
parameterization on tropical climate variability, Geophys. Res. Lett., 27,
3691–3694,
https://doi.org/10.1029/2000GL011964, 2000.
a
Mueller, E. A. and Stechmann, S. N.: Shallow-cloud impact on climate and
uncertainty: A simple stochastic model, Mathematics of Climate and Weather
Forecasting, 6, 16–37, 2020. a
Neelin, J. D., Sahany, S., Stechmann, S. N., and Bernstein, D. N.: Global
warming precipitation accumulation increases above the current-c limate
cutoff scale, P. Natl. Acad. Sci. USA, 114, 1258–1263,
https://doi.org/10.1073/pnas.1615333114, 2017.
a
Peters, O., Deluca, A., Corral, A., Neelin, J. D., and Holloway, C. E.:
Universality of rain event size distributions, J. Stat. Mech., 2010,
P11030,
https://doi.org/10.1088/1742-5468/2010/11/P11030, 2010.
a
Richardson, C. W.: Stochastic simulation of daily precipitation, temperature,
and solar radiation, Water Resour. Res., 17, 182–190, 1981. a
Sacerdote, L. and Giraudo, M. T.: Stochastic integrate and fire models: a
review on mathematical methods and their applications, in: Stochastic
biomathematical models, Springer, 99–148,
https://doi.org/10.1007/978-3-642-32157-3_5, 2013.
a,
b
Stechmann, S. N. and Neelin, J. D.: First-passage-time prototypes for
precipitation statistics, J. Atmos. Sci., 71, 3269–3291, 2014.
a,
b
Whitt, W.: Approximating a point process by a renewal process, I: Two basic
methods, Oper. Res., 30, 125–147, 1982. a
