Papers by Andrzej Święch

Stochastic optimal control in Hilbert spaces: $C^{1,1}$ regularity of the value function and optimal synthesis via viscosity solutions, F. De Feo, A. Swiech and L. Wessels, preprint, 2023.
Optimal control of stochastic delay differential equations: Optimal feedback controls, F. De Feo and A. Swiech, preprint, 2023.
Optimal control of stochastic delay differential equations and applications to path-dependent financial and economic models, F. De Feo, S. Federico and A. Swiech, to appear in SIAM J. Control Optim.
A fully nonlinear degenerate free transmission problem, G. Huaroto, E. A. Pimentel, G. C. Rampasso and A. Swiech, Ann. PDE 10, article number 5, (2024).
Finite dimensional approximations of Hamilton-Jacobi-Bellman equations for stochastic particle systems with common noise, S. Mayorga and A. Swiech, SIAM J. Control Optim. 61 (2023), no. 2, 820--851.
Aleksandrov-Bakelman-Pucci maximum principle for $L^p$-viscosity solutions of equations with unbounded terms, S. Koike and A. Swiech, J. Math. Pures Appl. (9) 168 (2022), 192--212.
Existence of solutions to a fully nonlinear free transmission problem, E. A. Pimentel and A. Swiech, J. Differential Equations 320 (2022), 49--63.
HJB Equation, Dynamic Programming Principle, and Stochastic Optimal Control, A. Swiech, Nonlinear Partial Differential Equations for Future Applications, Sendai, Japan, July 10--28 and October 2--6, 2017, S. Koike, H. Kozono, T. Ogawa, S. Sakaguchi, eds., Springer Proceedings in Mathematics and Statistics, vol. 346, 2021, Springer Singapore, 183--204.
Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures, W. Gangbo, S. Mayorga and A. Swiech, SIAM J. Math. Anal. 53 (2021), no. 2, 1320--1356.
Singular perturbations and optimal control of stochastic systems in infinite dimension: HJB equations and viscosity solutions, A. Swiech, ESAIM Control, Optim. Calc. Var. 27 (2021), Paper No. 6, 34 pp.
Viscosity solutions to an initial value problem for a Hamilton-Jacobi equation with a degenerate Hamiltonian occurring in the dynamics of peakons, T. Cieslak, J. Siemianowski and A. Swiech, Nonlinear Anal. 204 (2021), 112204, 25 pp.
Pointwise properties of $L^p$-viscosity solutions of uniformly elliptic equations with quadratically growing gradient terms, A. Swiech, Discrete Contin. Dyn. Syst. 40 (2020), no. 5, 2945--2962.
Viscosity solutions to HJB equations for boundary-noise and boundary-control problems, A. Swiech, SIAM J. Control Optim. 58 (2020), no. 1, 303--326.
Coupling Levy measures and comparison principles for viscosity solutions, N. Guillen, C. Mou and A. Swiech, Trans. Amer. Math. Soc. 372 (2019), no. 10, 7327--7370.
Stochastic representations for solutions to parabolic Dirichlet problems for nonlocal Bellman equations, R. Gong, C. Mou and A. Swiech, Ann. Appl. Probab. 29 (2019), no. 6, 3271--3310.
Weak Harnack inequality for fully nonlinear uniformly parabolic equations with unbounded ingredients and applications, S. Koike, A. Swiech and S. Tateyama, Nonlinear Anal. 185 (2019), 264--289.
A note on the upper perturbation property and removable sets for fully nonlinear degenerate elliptic PDE, A. Swiech, NoDEA Nonlinear Differential Equations Appl. 26 (2019), no. 1, Art. 3, 4 pp.
Corrigendum to "Aleksandrov-Bakelman-Pucci maximum principles for a class of uniformly elliptic and parabolic integro-PDE'' [J. Differential Equations 264 (2018) 2708--2736], C. Mou and A. Swiech, J. Differential Equations 265 (2018), no. 11, 5831.
Aleksandrov-Bakelman-Pucci maximum principles for a class of uniformly elliptic and parabolic integro-PDE, C. Mou and A. Swiech, J. Differential Equations 264 (2018), no. 4, 2708--2736.
Partial regularity of viscosity solutions for a class of Kolmogorov equations arising from mathematical finance, M. Rosestolato and A. Swiech, J. Differential Equations 262 (2017), no. 3, 1897--1930.
Integro-PDE in Hilbert spaces: Existence of viscosity solutions, A. Swiech and J. Zabczyk, Potential Anal. 45 (2016), no. 4, 703--736.
Scaling limits for conditional diffusion exit problems and asymptotics for nonlinear elliptic equations, Y. Bakhtin and A. Swiech, Trans. Amer. Math. Soc. 368 (2016), no. 9, 6487--6517.
Uniqueness of viscosity solutions for a class of integro-differential equations, C. Mou and A. Swiech, NoDEA Nonlinear Differential Equations Appl. 22 (2015), no. 6, 1851--1882.
Existence of a solution to an equation arising from the theory of Mean Field Games, W. Gangbo and A. Swiech, J. Differential Equations 259 (2015), no. 11, 6573--6643.
Metric viscosity solutions of Hamilton-Jacobi equations depending on local slopes, W. Gangbo and A. Swiech, Calc. Var. Partial Differential Equations 54 (2015), no. 1, 1183--1218.
Optimal transport and large number of particles, W. Gangbo and A. Swiech, Discrete Contin. Dyn. Syst. 34 (2014), no. 4, 1397--1441.
Representation formulas for solutions of Isaacs integro-PDE, S. Koike and A. Swiech, Indiana Univ. Math. J. 62 (2013), no. 5, 1473--1502.
Optimal control for a mixed flow of Hamiltonian and gradient type in space of probability measures, J. Feng and A. Swiech, with Appendix B by Atanas Stefanov, Trans. Amer. Math. Soc. 365 (2013), no. 8, 3987--4039.
Uniqueness for integro-PDE in Hilbert spaces, A. Swiech and J. Zabczyk, Potential Anal. 38 (2013), 233--259.
Local maximum principle for $L^p$-viscosity solutions of fully nonlinear elliptic PDEs with unbounded coefficients, S. Koike and A. Swiech, Commun. Pure Appl. Anal. 11 (2012), no. 5, 1897--1910.
Large deviations for stochastic PDE with Levy noise, A. Swiech and J. Zabczyk, J. Funct. Anal. 260 (2011), 674--723.
Sub- and superoptimality principles and construction of almost optimal strategies for differential games in Hilbert spaces, A. Swiech, Advances in Dynamic Games: Theory, Applications, and Numerical Methods for Differential and Stochastic Games, Annals of the International Society of Dynamic Games (M. Breton and K. Szajowski, eds.), Vol. 11, 149--163, Birkhauser, 2011.
Verification theorem and construction of $\epsilon$-optimal controls for control of abstract evolution equations, G. Fabbri, F. Gozzi and A. Swiech, J. Convex Anal. 17 (2010), no. 2, 611--642.
Erratum: ``A corrected proof of the stochastic verification theorem within the framework of viscosity solutions'', F. Gozzi, A. Swiech and X. Y. Zhou, SIAM J. Control Optim. 48 (2010), no. 6, 4177--4179.
Existence of strong solutions of Pucci extremal equations with superlinear growth in $Du$, S. Koike and A. Swiech, J. Fixed Point Theory Appl. 5 (2009), no. 2, 291--304.
Weak Harnack inequality for fully nonlinear uniformly elliptic PDE with unbounded ingredients, S. Koike and A. Swiech, J. Math. Soc. Japan. 61 (2009), no. 3, 723--755.
A PDE approach to large deviations in Hilbert spaces, A. Swiech, Stochastic Process. Appl. 119 (2009), no. 4, 1081--1123.
Regularity for obstacle problems in infinite dimensional Hilbert spaces, A. Swiech and E. V. Teixeira, Adv. Math. 220 (2009), no. 3, 964--983.
Maximum principle for fully nonlinear equations via the iterated comparison function method, S. Koike and A. Swiech, Math. Ann. 339 (2007), no. 2, 461--484.
Perron's method and the method of relaxed limits for ``unbounded" PDE in Hilbert spaces, D. Kelome and A. Swiech, Studia Math. 176 (2006), no. 3, 249--277.
Bellman equations associated to the optimal feedback control of stochastic Navier-Stokes equations, F. Gozzi, S. S. Sritharan and A. Swiech, Comm. Pure Appl. Math. 58 (2005), 671-700.
Uniqueness and existence of maximal and minimal solutions of fully nonlinear elliptic PDE, R. Jensen and A. Swiech, Comm. Pure Appl. Anal. 4 (2005), no. 1, 199--207.
A corrected proof of the stochastic verification theorem within the framework of viscosity solutions, F. Gozzi, A. Swiech and X. Y. Zhou, SIAM J. Control Optim. 43 (2005), no. 6, 2009--2019.
Maximum principle and existence of $L^p$-viscosity solutions for fully nonlinear uniformly elliptic equations with measurable and quadratic terms, S. Koike and A. Swiech, NoDEA Nonlinear Differential Equations Appl. 11 (2004), no. 4, 491-509.
A note on generalized maximum principles for elliptic and parabolic PDE, M. G. Crandall and A. Swiech, in Evolution Equations, Proceedings in honor of J. A. Goldstein's 60th birthday (Goldstein, Nagel and Romanelli eds.), Lecture notes in pure and applied mathematics, vol. 234, Marcel Dekker, 2003, 121--127.
Viscosity solutions of an infinite-dimensional Black-Scholes-Barenblatt equation, D. Kelome and A. Swiech, Appl. Math. Optim. 47 (2003), no. 3, 253--278.
Viscosity solutions of dynamic programming equations for the optimal control of Navier-Stokes equations, F. Gozzi, S.S. Sritharan, and A. Swiech, Arch. Ration. Mech. Anal. 163 (2002), no. 4, 295--327.
Risk-sensitive control and differential games in infinite dimensions, A. Swiech, Nonlinear Anal. 50 (2002), no. 4, Ser. A: Theory Methods, 509--522.
Good and viscosity solutions of fully nonlinear elliptic equations, R. Jensen, M. Kocan, and A. Swiech, Proc. Amer. Math. Soc. 130 (2002), no. 2, 533-542.
Hamilton-Jacobi-Bellman equations for the optimal control of the Duncan-Mortensen-Zakai equation, F. Gozzi, and A. Swiech, J. Funct. Anal. 172 (2000), no. 2, 466-510.
$L^p$-Theory for fully nonlinear uniformly parabolic equations, M.G. Crandall, M. Kocan, and A. Swiech, Comm. Partial Differential Equations 25 (2000), no. 11&12, 1997--2053.
Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations, M.G. Crandall, M. Kocan, P.L. Lions, and A. Swiech, Electron. J. Differential Equations, Vol. 1999 (1999), No. 24, 1--20.
Remarks on nonlinear, uniformly parabolic equations, M.G. Crandall, P. Fok, M. Kocan, and A. Swiech, Indiana Univ. Math. J. 47 (1998), no. 4, 1293--1326.
Second order Hamilton-Jacobi equations in Hilbert spaces and stochastic boundary control, F. Gozzi, E. Rouy, and A. Swiech, SIAM J. Control Optim. 38 (2000), no. 2, 400-430.
Incentive compatibility constraints and dynamic programming in continuous time, E. Barucci, F. Gozzi, and A. Swiech, Journal of Mathematical Economics 34 (2000), no. 4, 471--508.
Optimal stopping in Hilbert spaces and pricing of American options, D. Gatarek, and A. Swiech, Math. Methods Oper. Res. 50 (1999), 135--147.
$W^{1,p}$-Interior estimates for solutions of fully nonlinear, uniformly elliptic equations, A. Swiech, Adv. Differential Equations 2 (1997), no. 6, 1005--1027.
Optimal maps for the Multidimensional Monge-Kantorovich Problem, W. Gangbo, and A. Swiech, Comm. Pure Appl. Math. 51 (1998), no. 1, 23--45.
On differential games for infinite dimensional systems with nonlinear, unbounded operators, M. Kocan, P. Soravia, and A. Swiech, J. Math. Anal. Appl. 211 (1997), 395--423.
A note on the differences of the consecutive powers of operators, A. Swiech, Linear Operators, J. Janas, F. H. Szafraniec, and J. Zemanek (eds.), Banach Center Publ. vol. 38, Institute of Mathematics, Polish Academy of Sciences, Warsaw, 1997, 381--383.
Another approach to the existence of value functions of stochastic differential games, A. Swiech, J. Math. Anal. Appl. 204 (1996), no. 3, 884--897.
Least squares integration of one-dimensional codistributions with application to approximate feedback linearization, A. Banaszuk, J. Hauser, and A. Swiech, Math. Control Signals Systems 9 (1996), no. 3, 207--241.
Perturbed optimization on product spaces, M. Kocan and A. Swiech, Nonlinear Anal. 26 (1996), no. 1, 81--90.
On the equivalence of various weak notions of solutions of elliptic PDE's with measurable ingredients, M.G. Crandall, M. Kocan, P. Soravia, and A. Swiech, Progress in Elliptic and Parabolic PDE's (A. Alvino et al. eds.), Pitman Research Notes in Math., vol. 350, 1996, 136--162.
Sub- and superoptimality principles of dynamic programming revisited, A. Swiech, Nonlinear Anal. 26 (1996), 1429--1436.
On viscosity solutions of fully nonlinear equations with measurable ingredients, L. Caffarelli, M.G. Crandall, M. Kocan, and A. Swiech, Comm. Pure Appl. Math. 49 (1996), 365--397.
Second order unbounded parabolic equations in separated form, M. Kocan, and A. Swiech, Studia Math. 115 (1995), 291--310.
Unbounded second order partial differential equations in infinite dimensional Hilbert spaces, A. Swiech, Communications in Partial Differential Equations 19 (11&12) (1994), 1999-2036.
On partial sup-convolutions, a lemma of P.L. Lions and viscosity solutions in Hilbert spaces, M.G. Crandall, M. Kocan, and A. Swiech, Adv. Math. Sci. Appl. 3 (1993/4), 1--15.
Spectral characterization of operators with precompact orbit, A. Swiech, Studia Math. 96 (1990), no. 3, 277--282.
- Books:
  G. Fabbri, F. Gozzi and A. Swiech, Stochastic Optimal Control in Infinite Dimension: Dynamic Programming and HJB Equations, with a contribution by M. Fuhrman and G. Tessitore, Probability Theory and Stochastic Modelling, vol. 82, Springer, 2017.
  Errata to the book Stochastic Optimal Control in Infinite Dimension: Dynamic Programming and HJB Equations, G. Fabbri, F. Gozzi and A. Swiech, with a contribution by M. Fuhrman and G. Tessitore.