Donvil, Brecht I. C.; Muratore-Ginanneschi, Paolo On the unraveling of open quantum dynamics. (English) Zbl 1536.81101 Open Syst. Inf. Dyn. 30, No. 3, Article ID 2350015, 33 p. (2023). MSC: 81S22 62M07 35R60 81Q05 81Q70 81P15 81P73 65C05 46C05 47D07 81V73 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Yamada, Toshihiro A new algorithm for computing path integrals and weak approximation of SDEs inspired by large deviations and Malliavin calculus. (English) Zbl 1533.60083 Appl. Numer. Math. 187, 192-205 (2023). MSC: 60H07 60H35 91G20 60J60 65C30 × Cite Format Result Cite Review PDF Full Text: DOI
Epshteyn, Yekaterina; Liu, Chang; Liu, Chun; Mizuno, Masashi Local well-posedness of a nonlinear Fokker-Planck model. (English) Zbl 1514.35437 Nonlinearity 36, No. 3, 1890-1917 (2023). Reviewer: Zhuan Ye (Xuzhou) MSC: 35Q84 35A01 35A02 35K15 60J60 35B65 35R60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Zhang, Sheng-qiang; Meng, Xin-zhu Asymptotic analysis of a nonlinear stochastic eco-epidemiological system with feedback control. (English) Zbl 1513.34204 Appl. Math., Ser. B (Engl. Ed.) 37, No. 3, 317-339 (2022). MSC: 34C60 34F05 60J70 92D30 92D40 93B25 34D05 × Cite Format Result Cite Review PDF Full Text: DOI OA License
Akiyama, Naho; Yamada, Toshihiro A high order weak approximation for jump-diffusions using Malliavin calculus and operator splitting. (English) Zbl 1491.60078 Monte Carlo Methods Appl. 28, No. 2, 97-110 (2022). MSC: 60H07 60H35 65C05 65C30 91G60 × Cite Format Result Cite Review PDF Full Text: DOI
Kolokoltsov, V. N. The law of large numbers for quantum stochastic filtering and control of many-particle systems. (English. Russian original) Zbl 1471.81056 Theor. Math. Phys. 208, No. 1, 937-957 (2021); translation from Teor. Mat. Fiz. 208, No. 1, 97-121 (2021). MSC: 81S25 81Q93 81V70 81Q05 35R60 91A15 58J65 60F05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Carollo, Federico; Garrahan, Juan P.; Jack, Robert L. Large deviations at level 2.5 for Markovian open quantum systems: quantum jumps and quantum state diffusion. (English) Zbl 1492.82011 J. Stat. Phys. 184, No. 1, Paper No. 13, 46 p. (2021). Reviewer: Jinqiao Duan (Chicago) MSC: 82C31 81S22 60J76 60F10 35Q55 81Q05 35R60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License
Khodadadian, Amirreza; Parvizi, Maryam; Heitzinger, Clemens An adaptive multilevel Monte Carlo algorithm for the stochastic drift-diffusion-Poisson system. (English) Zbl 1462.65166 Comput. Methods Appl. Mech. Eng. 368, Article ID 113163, 23 p. (2020). MSC: 65M75 65M50 65M12 65M15 60H15 35R60 82D37 65C30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Debbi, Latifa Fractional stochastic active scalar equations generalizing the multi-dimensional quasi-geostrophic & 2D-Navier-Stokes equations: the general case. (English) Zbl 1467.58017 J. Math. Fluid Mech. 22, No. 4, Paper No. 54, 52 p. (2020). Reviewer: Jürgen Socolowsky (Brandenburg an der Havel) MSC: 58J65 60H15 35R11 35Q30 46B25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Baños, David R.; Duedahl, Sindre; Meyer-Brandis, Thilo; Proske, Frank Construction of Malliavin differentiable strong solutions of SDEs under an integrability condition on the drift without the Yamada-Watanabe principle. (English. French summary) Zbl 1404.60077 Ann. Inst. Henri Poincaré, Probab. Stat. 54, No. 3, 1464-1491 (2018). MSC: 60H10 60H07 60H40 60J60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Nenciu, Gheorghe; Nenciu, Irina Drift-diffusion equations on domains in \(\mathbb{R}^d\): essential self-adjointness and stochastic completeness. (English) Zbl 1404.35132 J. Funct. Anal. 273, No. 8, 2619-2654 (2017). Reviewer: Luigi Provenzano (Padova) MSC: 35J10 35Q41 35R60 60J25 81Q05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Neate, Andrew; Truman, Aubrey Semiclassical stochastic mechanics for the Coulomb potential with applications to modelling dark matter. (English) Zbl 1342.83543 J. Math. Phys. 57, No. 5, 052103, 26 p. (2016). MSC: 83F05 81Q20 81Q05 81P20 81S10 83C05 83C75 70F15 × Cite Format Result Cite Review PDF Full Text: DOI Link
Manca, Fabio; Déjardin, Pierre-Michel; Giordano, Stefano Statistical mechanics of holonomic systems as a Brownian motion on smooth manifolds. (English) Zbl 1351.82059 Ann. Phys., Berlin 528, No. 5, 381-393 (2016). Reviewer: Piotr Garbaczewski (Opole) MSC: 82C31 58J35 60J65 58J65 49S05 49J55 60H07 70H03 70H05 35Q84 × Cite Format Result Cite Review PDF Full Text: DOI
Duboscq, Romain A construction of the fundamental solution of the Schrödinger equation with a perturbed quadratic Hamiltonian. (English) Zbl 1337.35003 Nonlinearity 29, No. 2, 566-602 (2016). MSC: 35A08 35Q41 35Q55 37J40 35J10 35R60 81Q05 × Cite Format Result Cite Review PDF Full Text: DOI Link
Gusev, S. A. Minimizing the variance of estimate of mathematical expectation of a diffusion process functional by parametric transformation of the parabolic boundary value problem. (Russian, English) Zbl 1299.65009 Sib. Zh. Vychisl. Mat. 14, No. 2, 141-153 (2011); translation in Numer. Analysis Appl. 4, No. 2, 114-124 (2011). MSC: 65C30 60H15 60H35 60J60 35K20 65M06 35R60 × Cite Format Result Cite Review PDF Full Text: DOI
Klyatskin, Valery I. Lectures on dynamics of stochastic systems. Translated from the Russian by A. Vinogradov. Revised and extended ed. (English) Zbl 1233.93001 Amsterdam: Elsevier/Academic Press (ISBN 978-0-12-384966-3/hbk). xiv, 396 p. (2011). Reviewer: Tran Nhu Pham (Hanoi) MSC: 93-02 34F05 60H05 93C95 93E03 × Cite Format Result Cite Review PDF Full Text: Link
Gobet, Emmanuel; Labart, Céline Sharp estimates for the convergence of the density of the Euler scheme in small time. (English) Zbl 1188.65007 Electron. Commun. Probab. 13, 352-363 (2008). MSC: 65C30 60H07 60H10 65L20 60H35 60J60 × Cite Format Result Cite Review PDF Full Text: DOI EuDML EMIS
Cruzeiro, Ana Bela; Zhang, Xicheng Bismut type formulae for diffusion semigroups on Riemannian manifolds. (English) Zbl 1106.58015 Potential Anal. 25, No. 2, 121-130 (2006). Reviewer: Jacques Franchi (Strasbourg) MSC: 58J35 60H07 35B65 58J65 × Cite Format Result Cite Review PDF Full Text: DOI
Thaler, Horst The Doss trick on symmetric spaces. (English) Zbl 1078.43004 Lett. Math. Phys. 72, No. 2, 115-127 (2005). Reviewer: G. G. Vrănceanu (Bucureşti) MSC: 43A85 58J65 47D06 81Q05 × Cite Format Result Cite Review PDF Full Text: DOI
Cañizo, José A.; López, José Luis; Nieto, Juan Global \(L^{1}\) theory and regularity for the 3D nonlinear Wigner-Poisson-Fokker-Planck system. (English) Zbl 1039.35093 J. Differ. Equations 198, No. 2, 356-373 (2004). MSC: 35Q40 81Q05 82C31 35B65 82C70 × Cite Format Result Cite Review PDF Full Text: DOI
Thaler, Horst Solutions of Schrödinger equations on compact Lie groups via probabilistic methods. (English) Zbl 1012.22016 Potential Anal. 18, No. 2, 119-140 (2003). Reviewer: Neculai Papaghiuc (Iasi) MSC: 22E30 58J65 58J35 81Q05 × Cite Format Result Cite Review PDF Full Text: DOI
Gliklikh, Yu. E. Deterministic viscous hydrodynamics via stochastic analysis on groups of diffeomorphisms. (English) Zbl 1038.76015 Theory Stoch. Process. 8(24), No. 1-2, 98-105 (2002). Reviewer: A. D. Borisenko (Kyïv) MSC: 76D06 60H15 × Cite Format Result Cite Review PDF
Debussche, A.; Di Menza, L. Numerical resolution of stochastic focusing NLS equations. (English) Zbl 1001.65006 Appl. Math. Lett. 15, No. 6, 661-669 (2002). MSC: 65C30 35Q55 65M06 65M50 60H15 60H40 60H35 × Cite Format Result Cite Review PDF Full Text: DOI
Gliklikh, Yu. E. Viscous hydrodynamics through stochastic perturbations of flows of perfect fluids on groups of diffeomorphisms. (English) Zbl 1011.37045 Vestn. Voronezh. Gos. Univ., Ser. Fiz. Mat. 2001, No. 1, 81-89 (2001). MSC: 37K65 76D06 58J65 35Q30 76D05 58D30 37N20 × Cite Format Result Cite Review PDF
Stoica, Gheorghe Regular delay Langevin equation with degenerate diffusion coefficient. (English) Zbl 1045.60505 Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 41, No. 4, 289-294 (1998). MSC: 60H07 60H25 60H30 × Cite Format Result Cite Review PDF
Breuer, Heinz-Peter; Kappler, Bernd; Petruccione, Francesco Heisenberg picture operators in the quantum-state diffusion model. (English) Zbl 0912.60082 J. Phys. A, Math. Gen. 31, No. 7, L147-L151 (1998). MSC: 60H30 81V80 81Q05 65C99 81-08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fushchych, W. I.; Barannyk, L. L. Symmetry reduction as a method of generating solutions to systems of linear differential equations. (Ukrainian) Zbl 0892.58084 Dopov. Akad. Nauk Ukr. 1996, No. 12, 44-49 (1996). Reviewer: I.O.Parasyuk (Kyïv) MSC: 58J65 35C05 81Q05 35Q35 × Cite Format Result Cite Review PDF
Bondarev, B. V. Derivation of quantum kinetic equation from the Liouville-von Neumann equation. (English. Russian original) Zbl 0875.35087 Theor. Math. Phys. 100, No. 1, 826-833 (1994); translation from Teor. Mat. Fiz. 100, No. 1, 33-43 (1994). MSC: 35Q40 60H99 81Q05 × Cite Format Result Cite Review PDF Full Text: DOI
Tsuchiya, Masaaki On the oblique derivative problem for diffusion processes and diffusion equations with Hölder continuous coefficients. (English) Zbl 0810.60073 Trans. Am. Math. Soc. 346, No. 1, 257-281 (1994). MSC: 60J60 35K20 × Cite Format Result Cite Review PDF Full Text: DOI
Van Herwaarden, Onno A. Spread of pollution by dispersive groundwater flow. (English) Zbl 0804.35159 SIAM J. Appl. Math. 54, No. 1, 26-41 (1994). Reviewer: M.Capinski (Kraków) MSC: 35R60 35Q35 60J70 60G50 35C20 35J25 × Cite Format Result Cite Review PDF Full Text: DOI
Banasiak, J.; Mika, J. R. Asymptotic analysis of the Fokker-Planck equation related to Brownian motion. (English) Zbl 0795.35126 Math. Models Methods Appl. Sci. 4, No. 1, 17-33 (1994). MSC: 35Q72 35C20 82C31 60J65 × Cite Format Result Cite Review PDF Full Text: DOI
Djehiche, Boualem Bernstein processes and Pauli-type equations. (English) Zbl 0790.60097 Potential Anal. 2, No. 4, 349-370 (1993). MSC: 60K40 60J25 81Q05 81S40 35K05 60H10 60J60 60J75 81P20 × Cite Format Result Cite Review PDF Full Text: DOI
Makhno, S. Ya. The diffusion approximation for a class of random processes. (English. Russian original) Zbl 0835.60052 Theory Probab. Math. Stat. 46, 77-87 (1993); translation from Teor. Jmovirn. Mat. Stat. 46, 76-87 (1992). MSC: 60H10 60F17 × Cite Format Result Cite Review PDF
Herbst, Ira; Pitt, Loren Diffusion equation techniques in stochastic monotonicity and positive correlations. (English) Zbl 0688.60062 Probab. Theory Relat. Fields 87, No. 3, 275-312 (1991). MSC: 60J60 60E15 60K35 81Q05 81Q99 × Cite Format Result Cite Review PDF Full Text: DOI
Leizarowitz, Arie Controlled diffusion processes on infinite horizon with the overtaking criterion. (English) Zbl 0637.60055 Appl. Math. Optimization 17, No. 1, 61-78 (1988). Reviewer: F.Flandoli MSC: 60G35 60J60 93E20 49J55 × Cite Format Result Cite Review PDF Full Text: DOI
Blanchard, Ph.; Combe, Ph.; Sirugue, M.; Sirugue-Collin, M. Jump processes related to the two dimensional Dirac equation. (English) Zbl 0655.60069 Stochastic processes - mathematics and physics II, proc. 2nd BiBoS Symp., Bielefeld/Ger. 1985, Lect. Notes Math. 1250, 1-13 (1987). MSC: 60J70 81P20 60J75 × Cite Format Result Cite Review PDF
De, S. S. Stochastic model of population growth and spread. (English) Zbl 0617.92017 Bull. Math. Biol. 49, 1-11 (1987). MSC: 92D25 60J70 × Cite Format Result Cite Review PDF Full Text: DOI
Batteati, M. Stationary states of the semiclassical diffusion equation for a system in a blackbody radiation field. (English) Zbl 0619.35091 Hadronic J. 9, 35-54 (1986). MSC: 35Q99 81Q05 × Cite Format Result Cite Review PDF
Ng, S. K.; Caines, P. E. Nonlinear filtering in Riemannian manifolds. (English) Zbl 0625.60051 IMA J. Math. Control Inf. 2, 25-36 (1985). MSC: 60G35 58J65 60H10 × Cite Format Result Cite Review PDF Full Text: DOI
DeWitt-Morette, Cecile Path integration at the crossroad of stochastic and differential calculus. (English) Zbl 0525.53068 Gauge theory and gravitation, Proc. int. Symp., Nara/Jap. 1982, Lect. Notes Phys. 176, 166-170 (1983). MSC: 53C80 53D50 58J65 81Q05 55R10 × Cite Format Result Cite Review PDF
Vermes, Domokos Optimal control based on observations on the boundary. (English) Zbl 0506.93077 Stochastic differential systems, Proc. 2nd Conf., Bad Honnef 1982, Lect. Notes Control Inf. Sci. 43, 369-377 (1982). MSC: 93E20 49K45 60H10 49K30 60J60 × Cite Format Result Cite Review PDF
Elworthy, David; Truman, Aubrey The classical limit of quantum mechanics in a curved space background. (English) Zbl 0484.58030 Functional integration, Theory Appl., Proc. Colloq., Louvain-la- Neuve/Belgium 1979, 65-87 (1980). MSC: 58J65 81Q05 58D30 81S40 60J60 35Q99 × Cite Format Result Cite Review PDF
Duncan, T. E. The heat equation, the Kac formula and some index formulas. (English) Zbl 0426.58024 Partial differential equations and geometry, Proc. Park City Conf. 1977, Lect. Notes Pure Appl. Math. 48, 57-76 (1979). MSC: 58J20 58J35 58J60 58J65 58J70 × Cite Format Result Cite Review PDF
Mizrahi, Maurice M. Correspondence rules and path integrals. (English) Zbl 0412.58017 Feynman path integrals, Proc. int. Colloq., Marseille 1978, Lect. Notes Phys. 106, 234-253 (1979). MSC: 37J99 60J60 60G99 81Q05 81Q30 81S40 × Cite Format Result Cite Review PDF