Publications
Preprints

  • J. Ivanhoe, M. Salins, Preventing finite-time blowup in a constrained potential for reaction-diffusion equations, (2024), 18 pgs. arXiv:2406.15672.

  • 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.

Publications

  1. M. Salins, Solutions to the stochastic heat equation with polynomially growing multiplicative noise do not explode in the critical regime, to appear in Annals of Probability (2024), 17 pgs. arXiv:2309.04330.

  2. M. Salins and S. Tindel, Regularity of the law of solutions to the stochastic heat equation with non-Lipschitz reaction term, Stochastic Processes and their Applications 168 (2024) 104263. 24 pgs. arXiv:2302.10678.

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

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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 .

  20. 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.

  21. 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.

  22. 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.

  23. 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.

  24. 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 .

  25. 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.