Publications
Preprints

  • L. Chen, M. Foondun, J. Huang, M. Salins, Global solution for superlinear stochastic heat equation on Rd under Osgood-type conditions, (2023), 22 pgs. arXiv:2310.02153.

  • M. Salins, Solutions to the stochastic heat equation with polynomially growing multiplicative noise do not explode in the critical regime, (2023), 21 pgs. arXiv:2309.04330.

Publications
  1. M. Salins and S. Tindel, Regularity of the law of solutions to the stochastic heat equation with non-Lipschitz reaction term, to appear in Stochastic Processes and their Applications (2023), 34 pgs. arXiv:2302.10678.

  2. I. Gasteratos, M. Salins, and K. Spiliopoulos, Importance sampling for stochastic reaction-diffusion equations in the moderate deviation regime, to appear in Stochastics and Partial Differential Equations: Analysis and Computations (2023), 62 pgs. arXiv:2206.00646.

  3. I. Gasteratos, M. Salins, and K. Spiliopoulos, Moderate deviations for systems of slow-fast reaction-diffusion equations, Stochastics and Partial Differential Equations: Analysis and Compuations 11(2) (2023), pp. 503-598. arXiv:2101.00085.

  4. M. Salins and L. Setayeshgar, Uniform large deviations for a class of Burgers-type stochastic partial differential equations in any spatial dimension, Potential Analysis 58(1) (2023), pp. 181-201.

  5. M. Salins, Global solutions to the stochastic heat equation with superlinear accretive reaction term and superlinear multiplicative noise term on a bounded spatial domain, Transactions of the American Mathematical Society 375(11) (2022) pp. 8083-8099. arXiv:2110.10130.

  6. M. Salins, Global solutions for the stochastic reaction-diffusion equation with super-linear multiplicative noise and strong dissipativity, Electronic Journal of Probability 27 (2022), 17 pgs. arXiv:2107.04459.

  7. M. Salins, Existence and uniqueness of global solutions to the stochastic heat equation with super-linear drift on an unbounded spatial domain, Stochastics and Dynamics 22(5) (2021) 2250014, 30 pgs. arXiv:2106.13221.

  8. M. Salins, Systems of small-noise stochastic reaction-diffusion equations satisfy a large deviations principle that is uniform over all initial data, Stochastic Processes and Their Applications 142 (2021), pp. 159-194. arXiv:2008.01140.

  9. M. Salins and K. Spiliopoulos, Metastability and exit problems for systems of stochastic reaction-diffusion equations, The Annals of Probability 49(5) (2021), pp. 2317-2370. arXiv:1903.06038.

  10. M. Salins, Existence and uniqueness for the mild solution of the stochastic heat equation with non-Lipschitz drift on an unbounded spatial domain, Stochastics and Partial Differential Equations: Analysis and Computations 9(3) (2021), pp. 714-745. arXiv:2002.02016.

  11. C. Mueller, E. Neuman, M. Salins, and G. Truong, An improved uniqueness result for a system of stochastic differential equations related to the stochastic wave equation, Journal of Stochastic Analysis 1(2) (2020), pp. 1-7. arXiv:1909.05944.

  12. W. Hu, K. Spiliopoulos, M. Salins, Large deviations and averaging for systems of slow-fast stochastic reaction-diffusion equations, Stochastics and Partial Differential Equations: Analysis and Computation 7(4) (2019), pp. 808-874. arXiv:1710.02618.

  13. M. Salins, A. Budhiraja, and P. Dupuis, Uniform large deviation principles for Banach space valued stochastic evolution equations, Transactions of the American Mathematical Society 372(12) (2019), pp. 8363-8421. arXiv:1803.00648.

  14. M. Salins, Equivalences and counterexamples between several definitions of the uniform large deviations principle, Probability Surveys 16(1) (2019), pp. 99-142. arXiv:1712.07231.

  15. M. Salins, Smoluchowski-Kramers approximation for the damped stochastic wave equation with multiplicative noise in any spatial dimension, Stochastic and Partial Differential Equations: Analysis and Computation 7(1) (2019), pp.86-122. arXiv:1801.10538.

  16. A. Gomez, J.J. Lee, C. Mueller, E. Neuman, and M. Salins, On Uniquness and blowup properties for a class of second order SDEs, Electronic Journal of Probability 22(72) (2017), pp. 1-17. arXiv:1702.07419.

  17. M. Salins, K. Spiliopoulos, Rare event simulation via importance sampling for linear SPDE's, Stochastics and Partial Differential Equations: Analysis and Compuation 5(4) (2017), pp. 652-690. arXiv:1609.04365.

  18. Z. Pajor-Gyulai, M. Salins, On dynamical systems perturbed by a null-recurrent motion: The general case, Stochastic Processes and their Applications 127(6) (2017), pp. 1960-1997. arXiv:1508.05346 .

  19. S. Cerrai, M. Freidlin, M. Salins, On the Smoluchowski-Kramers approximation for SPDEs and its interplay with large deviations and long time behavior, Discrete and Continuous Dynamical Systems 37(1) (2017), pp. 33-76. arXiv:1602:04279.

  20. S. Cerrai, M. Salins, On the Smoluchowski-Kramers approximation for a system with infinite degrees of freedom exposed to a magnetic field, Stochastic Processes and their Applications 127(1) (2017), pp. 273-303. arXiv:1409.0803.

  21. M. Salins and K. Spiliopoulos, Markov processes with spatial delay: path space characterization, occupation time and properties, Stochastics and Dynamics 17(06) (2016), 24 pgs. arXiv:1601:03759.

  22. S. Cerrai, M. Salins, Smoluchowski-Kramers approximation and large deviations for a general non-gradient system with an infinite number of degrees of freedom, Annals of Probability 44(4) (2016), 2591-2642. arXiv:1403.5745.

  23. Z. Pajor-Gyulai, M. Salins, On dynamical systems with perturbation driven by a null-recurrent fast motion: the continuous coefficient case, Journal of Theoretical Probability 29(3) (2016), pp. 1083-1099. arXiv:1410:4625 .

  24. S. Cerrai, M. Salins, Smoluchowski-Kramers approximation and large deviations for infinite dimensional gradient systems, Asymptotic Analysis 88(4) (2014), pp. 201-215. arXiv:1403.5743.