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## Search Articles

2015, Mathematical surveys and monographs, ISBN 1470425580, Volume 207, xii, 479

Book

Nonlinear analysis, ISSN 0362-546X, 11/2015, Volume 128, pp. 199 - 226

We study uniqueness of families of probability measures solving the Cauchy problem for nonlinear Fokker–Planck–Kolmogorov equation with unbounded coefficients....

Nonlinear Fokker–Planck–Kolmogorov equation | McKean–Vlasov equation | Uniqueness of solutions to the Cauchy problem for nonlinear parabolic equations | Nonlinear Fokker-Planck-Kolmogorov equation | Uniqueness of solutions to the | Cauchy problem for nonlinear parabolic equations | McKean-Vlasov equation | Nonlinearity | Construction | Mathematical analysis | Uniqueness | Cauchy problem

Nonlinear Fokker–Planck–Kolmogorov equation | McKean–Vlasov equation | Uniqueness of solutions to the Cauchy problem for nonlinear parabolic equations | Nonlinear Fokker-Planck-Kolmogorov equation | Uniqueness of solutions to the | Cauchy problem for nonlinear parabolic equations | McKean-Vlasov equation | Nonlinearity | Construction | Mathematical analysis | Uniqueness | Cauchy problem

Journal Article

Journal of dynamics and differential equations, ISSN 1040-7294, 6/2016, Volume 28, Issue 2, pp. 493 - 518

... on Arbitrary Domains
Oxana A. Manita 1 · Stanislav V . Shaposhnikov 1 , 2
Received: 2 August 2014 / Revised: 8 April 2015 / Published online: 21 April 2015
© Springer...

Ordinary Differential Equations | Fokker–Planck–Kolmogorov equation | 60J60 | Diffusion process | Mathematics | Applications of Mathematics | 35K12 | 60J35 | Partial Differential Equations | 47D07 | Cauchy problem | 35K10 | Physical Sciences | Mathematics, Applied | Science & Technology

Ordinary Differential Equations | Fokker–Planck–Kolmogorov equation | 60J60 | Diffusion process | Mathematics | Applications of Mathematics | 35K12 | 60J35 | Partial Differential Equations | 47D07 | Cauchy problem | 35K10 | Physical Sciences | Mathematics, Applied | Science & Technology

Journal Article

Probability theory and related fields, ISSN 1432-2064, 02/2013, Volume 158, Issue 1-2, pp. 465 - 476

... I. Bogachev · Michael Röckner ·
Stanislav V . Shaposhnikov
Received: 30 August 2012 / Revised: 20 November 2012 / Accepted: 15 January 2013 /
Published online: 1 February...

60J75 | Absolute continuity | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Quantitative Finance | Diffusion with jumps | Secondary 35K25 | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | Transition probability | Primary 60J60 | Statistics & Probability | Physical Sciences | Science & Technology | Studies | Probability | Diffusion | Mathematical analysis | Continuity

60J75 | Absolute continuity | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Quantitative Finance | Diffusion with jumps | Secondary 35K25 | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | Transition probability | Primary 60J60 | Statistics & Probability | Physical Sciences | Science & Technology | Studies | Probability | Diffusion | Mathematical analysis | Continuity

Journal Article

Journal of evolution equations, ISSN 1424-3199, 06/2020, Volume 20, Issue 2, pp. 355 - 374

We prove a formula representing solutions to parabolic Fokker-Planck-Kolmogorov equations with coefficients of low regularity. This formula is applied for...

Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Coefficients | Mathematical analysis | Upper bounds | Formulas (mathematics) | Regularity

Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Coefficients | Mathematical analysis | Upper bounds | Formulas (mathematics) | Regularity

Journal Article

Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, ISSN 1120-6330, 01/2019, Volume 30, Issue 1, pp. 205 - 221

We prove two new results connected with elliptic Fokker-Planck-Kolmogorov equations with drifts integrable with respect to solutions. The first result answers...

Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Journal of functional analysis, ISSN 0022-1236, 06/2019, Volume 276, Issue 12, pp. 3681 - 3713

We study convergence in variation of probability solutions of nonlinear Fokker–Planck–Kolmogorov equations to stationary solutions. We obtain sufficient...

Stationary measure | Exponential convergence | Nonlinear Fokker–Planck–Kolmogorov equation | Physical Sciences | Mathematics | Science & Technology

Stationary measure | Exponential convergence | Nonlinear Fokker–Planck–Kolmogorov equation | Physical Sciences | Mathematics | Science & Technology

Journal Article

Annali di matematica pura ed applicata, ISSN 0373-3114, 10/2017, Volume 196, Issue 5, pp. 1609 - 1635

... I. Bogachev 1 · Stanislav V . Shaposhnikov 1
Received: 12 May 2016 / Accepted: 24 December 2016 / Published online: 4 January 2017
© Fondazione Annali di Matematica Pura...

Harnack’s inequality | Primary 35J15 | Secondary 35B65 | Mathematics, general | Mathematics | Double divergence form equation | Continuity of solutions | Stationary Fokker–Planck–Kolmogorov equation | Physical Sciences | Mathematics, Applied | Science & Technology | Continuity | Divergence | Integral calculus | Mathematical analysis

Harnack’s inequality | Primary 35J15 | Secondary 35B65 | Mathematics, general | Mathematics | Double divergence form equation | Continuity of solutions | Stationary Fokker–Planck–Kolmogorov equation | Physical Sciences | Mathematics, Applied | Science & Technology | Continuity | Divergence | Integral calculus | Mathematical analysis

Journal Article

Nonlinear analysis, ISSN 0362-546X, 11/2015, Volume 128, pp. 199 - 226

We study uniqueness of families of probability measures solving the Cauchy problem for nonlinear Fokker Planck Kolmogorov equation with unbounded coefficients....

Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Journal of dynamics and differential equations, ISSN 1572-9222, 02/2020

We prove a generalization of the known result of Trevisan on the Ambrosio-FigalliTrevisan superposition principle for probability solutions to the Cauchy...

Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Journal of clinical oncology, ISSN 0732-183X, 05/2020, Volume 38, Issue 15_suppl, pp. e16695 - e16695

e16695 Background: 90% of pancreatic cancers are adenocarcinomas. Pancreatic neuroendocrine tumors (PNET) are much less common. However, some adenocarcinomas...

Journal Article

Discrete and continuous dynamical systems, ISSN 1078-0947, 07/2016, Volume 36, Issue 7, pp. 3519 - 3543

We obtain sufficient conditions for the differentiability of solutions to stationary Fokker-Planck-Kolmogorov equations with respect to a parameter. In...

Stationary Fokker-Planck-Kolmogorov equation | Differentiability with respect to a parameter | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Stationary Fokker-Planck-Kolmogorov equation | Differentiability with respect to a parameter | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

07/2018, Springer Proceedings in Mathematics & Statistics, ISBN 9783319749280, Volume 229

ExistenceShaposhnikov, Stanislav and uniqueness of solutions of the Cauchy problem for nonlinear Fokker–Planck...

Nonlinear Fokker–Planck–Kolmogorov equation | McKean–Vlasov equation | 35Q84 | 35Q83 | 35K55 | Existence and uniqueness of solutions to the Cauchy problem for nonlinear parabolic equations

Nonlinear Fokker–Planck–Kolmogorov equation | McKean–Vlasov equation | 35Q84 | 35Q83 | 35K55 | Existence and uniqueness of solutions to the Cauchy problem for nonlinear parabolic equations

Book Chapter

Journal of functional analysis, ISSN 0022-1236, 2008, Volume 254, Issue 10, pp. 2690 - 2705

We consider the set of all probability measures
μ on
R
d
satisfying an elliptic equation
L
∗
μ
=
0
in the weak worm. We give sufficient conditions in order...

Nonuniqueness | Elliptic equation for measures | Physical Sciences | Mathematics | Science & Technology

Nonuniqueness | Elliptic equation for measures | Physical Sciences | Mathematics | Science & Technology

Journal Article

03/2019

We prove a generalization of the known result of Trevisan on the
Ambrosio-Figalli-Trevisan superposition principle for probability solutions to
the Cauchy...

Mathematics - Probability

Mathematics - Probability

Journal Article

07/2013

We consider Fokker--Planck--Kolmogorov equations with unbounded coefficients
and obtain upper estimates of solutions. We also obtain new estimates involving...

Mathematics - Analysis of PDEs

Mathematics - Analysis of PDEs

Journal Article

03/2018

We prove two new results connected with elliptic Fokker-Planck-Kolmogorov
equations with drifts integrable with respect to solutions. The first result
answers...

Mathematics - Probability

Mathematics - Probability

Journal Article

Annali della Scuola normale superiore di Pisa, Classe di scienze, ISSN 0391-173X, 01/2015, Volume 14, Issue 3, pp. 983 - 1023

We prove a new uniqueness result for solutions to Fokker-Planck-Kolmogorov (FPK) equations for probability measures on infinite-dimensional spaces. We consider...

Physical Sciences | Mathematics | Science & Technology

Physical Sciences | Mathematics | Science & Technology

Journal Article

07/2013

We study the Cauchy problem for Fokker--Planck--Kolmogorov equations with
unbounded and degenerate coefficients. Sufficient conditions for the existence
and...

Mathematics - Analysis of PDEs

Mathematics - Analysis of PDEs

Journal Article

Journal of evolution equations, ISSN 1424-3199, 9/2013, Volume 13, Issue 3, pp. 577 - 593

... Equations
On uniqueness of solutions to the Cauchy problem for degenerate
Fokker–Planck–Kolmogorov equations
Vladimir I. Bogachev, Michael R ¨ ockner and
Stanislav V...

Degenerate parabolic equation | Analysis | Uniqueness | Mathematics | 35K15 | 35K67 | 35K10 | 35K65 | Cauchy problem | Physical Sciences | Mathematics, Applied | Science & Technology

Degenerate parabolic equation | Analysis | Uniqueness | Mathematics | 35K15 | 35K67 | 35K10 | 35K65 | Cauchy problem | Physical Sciences | Mathematics, Applied | Science & Technology

Journal Article

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