Journal articles: 'Singular drift'

1

Jakubowski, Tomasz. "Fractional Laplacian with singular drift." Studia Mathematica 207, no. 3 (2011): 257–73. http://dx.doi.org/10.4064/sm207-3-3.

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2

Bass, Richard F., and Zhen-Qing Chen. "Brownian motion with singular drift." Annals of Probability 31, no. 2 (2003): 791–817. http://dx.doi.org/10.1214/aop/1048516536.

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3

Kim, Panki, and Renming Song. "Stable process with singular drift." Stochastic Processes and their Applications 124, no. 7 (July 2014): 2479–516. http://dx.doi.org/10.1016/j.spa.2014.03.006.

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4

REZNIK, GREGORY, and ZIV KIZNER. "Two-layer quasi-geostrophic singular vortices embedded in a regular flow. Part 2. Steady and unsteady drift of individual vortices on a beta-plane." Journal of Fluid Mechanics 584 (July 25, 2007): 203–23. http://dx.doi.org/10.1017/s0022112007006404.

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Drift of individual β-plane vortices confined to one layer of a two-layer fluid under the rigid-lid condition is considered. For this purpose, the theory of two-layer quasi-geostrophic singular vortices is employed. On a β-plane, any non-zonal displacement of a singular vortex results in the development of a regular flow. An individual singular β-plane vortex cannot be steady on its own: the vortex moves coexisting with a regular flow, be the drift steady or not. In this paper, both kinds of drift of a singular vortex are considered. A new steady exact solution is presented, a hybrid regular–singular modon. This hybrid modon consists of a dipole component and a circularly symmetric rider. The dipole is regular, and the rider is a superposition of the singular vortex and a regular circularly symmetric field. The unsteady drift of a singular vortex residing in one of the layers is considered under the condition that, at the initial instant, the regular field is absent. The development of barotropic and baroclinic regular β-gyres is examined. Whereas the barotropic and baroclinic modes of the singular vortex are comparable in magnitudes, the baroclinic β-gyres attenuate with time, making the trajectory of the vortex close to that of a barotropic monopole on a β-plane.

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5

Blanchard, Philippe, and Simon Golin. "Diffusion processes with singular drift fields." Communications in Mathematical Physics 109, no. 3 (September 1987): 421–35. http://dx.doi.org/10.1007/bf01206145.

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6

Rutkowski, Marek. "Stochastic differential equations with singular drift." Statistics & Probability Letters 10, no. 3 (August 1990): 225–29. http://dx.doi.org/10.1016/0167-7152(90)90078-l.

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7

Kinzebulatov, D., and K. R. Madou. "Stochastic equations with time-dependent singular drift." Journal of Differential Equations 337 (November 2022): 255–93. http://dx.doi.org/10.1016/j.jde.2022.07.042.

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8

Jin, Peng. "Brownian Motion with Singular Time-Dependent Drift." Journal of Theoretical Probability 30, no. 4 (May 2, 2016): 1499–538. http://dx.doi.org/10.1007/s10959-016-0687-3.

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9

Labed, Saloua. "MAXIMUM PRINCIPLE FOR SINGULAR CONTROL PROBLEMS OF SYSTEMS DRIVEN BY MARTINGALE MEASURES." Advances in Mathematics: Scientific Journal 12, no. 1 (January 23, 2023): 193–216. http://dx.doi.org/10.37418/amsj.12.1.13.

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We provide necessary optimality conditions for singular controlled stochastic differential equations driven by an orthogonal continuous martingale measure. The control is allowed to enter both the drift and diffusion coefficient and has two components, the first being relaxed and the second singular, the domain of the first control does not need to be convex, and for the relaxing method, we show by a counter-example that replacing the drift and diffusion coefficients by their relaxed counterparts does not define a true relaxed control problem. The maximum principle for these systems is established by means of spike variation techniques on the relaxed part of the control and a convex perturbation on the singular one. Our result is a generalization of Peng's maximum principle to singular control problems.

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10

NISHIBATA, SHINYA, NAOTAKA SHIGETA, and MASAHIRO SUZUKI. "ASYMPTOTIC BEHAVIORS AND CLASSICAL LIMITS OF SOLUTIONS TO A QUANTUM DRIFT-DIFFUSION MODEL FOR SEMICONDUCTORS." Mathematical Models and Methods in Applied Sciences 20, no. 06 (June 2010): 909–36. http://dx.doi.org/10.1142/s0218202510004477.

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This paper discusses a time global existence, asymptotic behavior and a singular limit of a solution to the initial boundary value problem for a quantum drift-diffusion model of semiconductors over a one-dimensional bounded domain. Firstly, we show a unique existence and an asymptotic stability of a stationary solution for the model. Secondly, it is shown that the time global solution for the quantum drift-diffusion model converges to that for a drift-diffusion model as the scaled Planck constant tends to zero. This singular limit is called a classical limit. Here these theorems allow the initial data to be arbitrarily large in the suitable Sobolev space. We prove them by applying an energy method.

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11

Huang, Xing. "Strong solutions for functional SDEs with singular drift." Stochastics and Dynamics 18, no. 02 (December 11, 2017): 1850015. http://dx.doi.org/10.1142/s0219493718500156.

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By using Zvonkin type transforms, existence and uniqueness are proved for a class of functional stochastic differential equations with singular drifts. The main results extend corresponding ones in [5, 11] for stochastic differential equations driven by Brownian motion and symmetric [Formula: see text]-stable process respectively.

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12

Aebi, Robert. "Diffusions with singular drift related to wave functions." Probability Theory and Related Fields 96, no. 1 (March 1993): 107–21. http://dx.doi.org/10.1007/bf01195885.

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13

Ling, Chengcheng, Sebastian Riedel, and Michael Scheutzow. "A Wong-Zakai theorem for SDEs with singular drift." Journal of Differential Equations 326 (July 2022): 344–63. http://dx.doi.org/10.1016/j.jde.2022.04.023.

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14

Qian, Zhongmin, and Guangyu Xi. "Parabolic equations with singular divergence‐free drift vector fields." Journal of the London Mathematical Society 100, no. 1 (December 6, 2018): 17–40. http://dx.doi.org/10.1112/jlms.12202.

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15

Höhnle, Rainer. "Construction of local solutions to sde's with singular drift." Stochastics and Stochastic Reports 47, no. 3-4 (April 1994): 163–92. http://dx.doi.org/10.1080/17442509408833889.

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16

Marinelli, Carlo, and Luca Scarpa. "A variational approach to dissipative SPDEs with singular drift." Annals of Probability 46, no. 3 (May 2018): 1455–97. http://dx.doi.org/10.1214/17-aop1207.

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17

Chen, Zhen-Qing, Shizan Fang, and Tusheng Zhang. "Small time asymptotics for Brownian motion with singular drift." Proceedings of the American Mathematical Society 147, no. 8 (March 21, 2019): 3567–78. http://dx.doi.org/10.1090/proc/14511.

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18

Yan, Jiaan. "On the existence of diffusions with singular drift coefficient." Acta Mathematicae Applicatae Sinica 4, no. 1 (February 1988): 23–29. http://dx.doi.org/10.1007/bf02018710.

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19

Nagasawa, Masao, and Hiroshi Tanaka. "A diffusion process in a singular mean-drift-field." Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete 68, no. 3 (1985): 247–69. http://dx.doi.org/10.1007/bf00532640.

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20

Brahim, Hafida Ben, Hanane Ben Gherbal, and Boulakhras Gherbal. "A necessary conditions for optimal singular control of McKean-Vlasov stochastic differential equations driven by spatial parameters local martingale." STUDIES IN ENGINEERING AND EXACT SCIENCES 5, no. 2 (July 19, 2024): e5926. http://dx.doi.org/10.54021/seesv5n2-036.

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In this paper, we focus on stochastic singular control problems involving McKean-Vlasov stochastic differential equations driven by a spatially parameterized continuous local martingale. The drift coefficient in these equations depends on the state of the solution process and its law. The control variable consists of two components: an absolutely continuous control and a singular one. Firstly, under Lipschitz conditions, we establish the existence and uniqueness of its strong solution. Next, we derive the necessary conditions for optimal singular control under the assumption that the control domain is convex. These optimality conditions differ from the classical ones in the sense that here the adjoint equation is a McKean-Vlasov backward stochastic differential equation driven by a continuous local martingale with spatial parameters. The proof of our result is based on the derivatives of the local martingale with respect to spatial parameters and the derivative of the drift coefficient with respect to the probability measure.

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21

Siddiqui, Maryam, Mhamed Eddahbi, and Omar Kebiri. "Numerical Solutions of Stochastic Differential Equations with Jumps and Measurable Drifts." Mathematics 11, no. 17 (August 31, 2023): 3755. http://dx.doi.org/10.3390/math11173755.

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This paper deals with numerical analysis of solutions to stochastic differential equations with jumps (SDEJs) with measurable drifts that may have quadratic growth. The main tool used is the Zvonkin space transformation to eliminate the singular part of the drift. More precisely, the idea is to transform the original SDEJs to standard SDEJs without singularity by using a deterministic real-valued function that satisfies a second-order differential equation. The Euler–Maruyama scheme is used to approximate the solution to the equations. It is shown that the rate of convergence is 12. Numerically, two different methods are used to approximate solutions for this class of SDEJs. The first method is the direct approximation of the original equation using the Euler–Maruyama scheme with specific tests for the evaluation of the singular part at simulated values of the solution. The second method consists of taking the inverse of the Euler–Maruyama approximation for Zvonkin’s transformed SDEJ, which is free of singular terms. Comparative analysis of the two numerical methods is carried out. Theoretical results are illustrated and proved by means of an example.

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22

Bachmann, Stefan. "Well-posedness and stability for a class of stochastic delay differential equations with singular drift." Stochastics and Dynamics 18, no. 02 (December 11, 2017): 1850019. http://dx.doi.org/10.1142/s0219493718500193.

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23

Le, Nam Q. "On the Harnack inequality for degenerate and singular elliptic equations with unbounded lower order terms via sliding paraboloids." Communications in Contemporary Mathematics 20, no. 01 (October 23, 2017): 1750012. http://dx.doi.org/10.1142/s0219199717500122.

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We use the method of sliding paraboloids to establish a Harnack inequality for linear, degenerate and singular elliptic equation with unbounded lower order terms. The equations we consider include uniformly elliptic equations and linearized Monge–Ampère equations. Our argument allows us to prove the doubling estimate for functions which, at points of large gradient, are solutions of (degenerate and singular) elliptic equations with unbounded drift.

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24

Blei, Stefan, and Hans-Jürgen Engelbert. "One-dimensional stochastic differential equations with generalized and singular drift." Stochastic Processes and their Applications 123, no. 12 (December 2013): 4337–72. http://dx.doi.org/10.1016/j.spa.2013.06.014.

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25

Krylov, N. V., and M. R�ckner. "Strong solutions of stochastic equations with singular time dependent drift." Probability Theory and Related Fields 131, no. 2 (May 25, 2004): 154–96. http://dx.doi.org/10.1007/s00440-004-0361-z.

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26

Kim, Inwon, Norbert Požár, and Brent Woodhouse. "Singular limit of the porous medium equation with a drift." Advances in Mathematics 349 (June 2019): 682–732. http://dx.doi.org/10.1016/j.aim.2019.04.017.

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27

Hofmann, Steve, and John L. Lewis. "The Dirichlet problem for parabolic operators with singular drift terms." Memoirs of the American Mathematical Society 151, no. 719 (2001): 0. http://dx.doi.org/10.1090/memo/0719.

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28

Huang, Xing, and Feng-Yu Wang. "Degenerate SDEs with singular drift and applications to Heisenberg groups." Journal of Differential Equations 265, no. 6 (September 2018): 2745–77. http://dx.doi.org/10.1016/j.jde.2018.04.050.

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29

Höhnle, Rainer. "On Global Existence of Solutions of SDE's with Singular Drift." Mathematische Nachrichten 179, no. 1 (1996): 145–60. http://dx.doi.org/10.1002/mana.19961790110.

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30

GASSER, INGENUIN, C. DAVID LEVERMORE, PETER A. MARKOWICH, and CHRISTIAN SCHMEISER. "The initial time layer problem and the quasineutral limit in the semiconductor drift-diffusion model." European Journal of Applied Mathematics 12, no. 4 (August 2001): 497–512. http://dx.doi.org/10.1017/s0956792501004533.

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The classical time-dependent drift-diffusion model for semiconductors is considered for small scaled Debye length (which is a singular perturbation parameter). The corresponding limit is carried out on both the dielectric relaxation time scale and the diffusion time scale. The latter is a quasineutral limit, and the former can be interpreted as an initial time layer problem. The main mathematical tool for the analytically rigorous singular perturbation theory of this paper is the (physical) entropy of the system.

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31

Baur, Benedict, and Martin Grothaus. "Skorokhod decomposition for a reflected -strong Feller diffusion with singular drift." Stochastics 90, no. 4 (September 16, 2017): 539–68. http://dx.doi.org/10.1080/17442508.2017.1371178.

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32

Zhang, Xicheng. "Strong solutions of SDES with singular drift and Sobolev diffusion coefficients." Stochastic Processes and their Applications 115, no. 11 (November 2005): 1805–18. http://dx.doi.org/10.1016/j.spa.2005.06.003.

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33

Mooney, Connor. "Harnack inequality for degenerate and singular elliptic equations with unbounded drift." Journal of Differential Equations 258, no. 5 (March 2015): 1577–91. http://dx.doi.org/10.1016/j.jde.2014.11.006.

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34

Jakubowski, T. "Fundamental Solution of the Fractional Diffusion Equation with a Singular Drift*." Journal of Mathematical Sciences 218, no. 2 (August 27, 2016): 137–53. http://dx.doi.org/10.1007/s10958-016-3016-6.

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35

Zhang, Xicheng. "Stochastic differential equations with Sobolev diffusion and singular drift and applications." Annals of Applied Probability 26, no. 5 (October 2016): 2697–732. http://dx.doi.org/10.1214/15-aap1159.

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36

Chamorro, Diego, and Stéphane Menozzi. "Fractional operators with singular drift: smoothing properties and Morrey–Campanato spaces." Revista Matemática Iberoamericana 32, no. 4 (2016): 1445–99. http://dx.doi.org/10.4171/rmi/925.

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37

Alvarado, Ryan, Dan Brigham, Vladimir Maz'ya, Marius Mitrea, and Elia Ziadé. "Sharp Geometric Maximum Principles for Semi-Elliptic Operators with Singular Drift." Mathematical Research Letters 18, no. 4 (2011): 613–20. http://dx.doi.org/10.4310/mrl.2011.v18.n4.a3.

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38

Lynch, S., and C. Knessl. "Singular perturbation analysis of drift-diffusion past a circle: shadow region." IMA Journal of Applied Mathematics 77, no. 2 (May 27, 2011): 252–78. http://dx.doi.org/10.1093/imamat/hxr022.

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39

Eberle, Andreas. "Lp Uniqueness of Non-symmetric Diffusion Operators with Singular Drift Coefficients." Journal of Functional Analysis 173, no. 2 (June 2000): 328–42. http://dx.doi.org/10.1006/jfan.2000.3574.

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40

De Angelis, Tiziano. "Optimal dividends with partial information and stopping of a degenerate reflecting diffusion." Finance and Stochastics 24, no. 1 (October 18, 2019): 71–123. http://dx.doi.org/10.1007/s00780-019-00407-1.

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Abstract We study the optimal dividend problem for a firm’s manager who has partial information on the profitability of the firm. The problem is formulated as one of singular stochastic control with partial information on the drift of the underlying process and with absorption. In the Markovian formulation, we have a two-dimensional degenerate diffusion whose first component is singularly controlled. Moreover, the process is absorbed when its first component hits zero. The free boundary problem (FBP) associated to the value function of the control problem is challenging from the analytical point of view due to the interplay of degeneracy and absorption. We find a probabilistic way to show that the value function of the dividend problem is a smooth solution of the FBP and to construct an optimal dividend strategy. Our approach establishes a new link between multidimensional singular stochastic control problems with absorption and problems of optimal stopping with ‘creation’. One key feature of the stopping problem is that creation occurs at a state-dependent rate of the ‘local time’ of an auxiliary two-dimensional reflecting diffusion.

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41

DUNN, D. C., N. R. McDONALD, and E. R. JOHNSON. "The motion of a singular vortex near an escarpment." Journal of Fluid Mechanics 448 (November 26, 2001): 335–65. http://dx.doi.org/10.1017/s0022112001006115.

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McDonald (1998) has studied the motion of an intense, quasi-geostrophic, equivalent-barotropic, singular vortex near an infinitely long escarpment. The present work considers the remaining cases of the motion of weak and moderate intensity singular vortices near an escarpment. First, the limit that the vortex is weak is studied using linear theory. For times which are short compared to the advective time scale associated with the vortex it is found that topographic waves propagate rapidly away from the vortex and have no leading-order influence on the vortex drift velocity. The vortex propagates parallel to the escarpment in the sense of its image in the escarpment. The mechanism for this motion is identified and is named the pseudoimage of the vortex. Large-time asymptotic results predict that vortices which move in the same direction as the topographic waves radiate non-decaying waves and drift slowly towards the escarpment in response to wave radiation. Vortices which move in the opposite direction to the topographic waves reach a steadily propagating state. Contour dynamics results reinforce the linear theory in the limit that the vortex is weak, and show that the linear theory is less robust for vortices which move counter to the topographic waves. Second, contour dynamics results for a moderate intensity vortex are given. It is shown that dipole formation is a generic feature of the motion of moderate intensity vortices and induces enhanced motion in the direction perpendicular to the escarpment.

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42

Eddahbi, Mhamed. "Well-Posedness of Backward Stochastic Differential Equations with Jumps and Irregular Coefficients." Fractal and Fractional 8, no. 1 (December 29, 2023): 26. http://dx.doi.org/10.3390/fractalfract8010026.

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In this paper, we focus on investigating the well-posedness of backward stochastic differential equations with jumps (BSDEJs) driven by irregular coefficients. We establish new results regarding the existence and uniqueness of solutions for a specific class of singular BSDEJs. Unlike previous studies, our approach considers terminal data that are square-integrable, eliminating the need for them to be necessarily bounded. The generators in our study encompass a standard drift, a signed measure across the entire real line, and the local time of the unknown process. This broadens the scope to include BSDEJs with quadratic growth in the Brownian component and exponential growth concerning the jump noise. The key methodology involves establishing Krylov-type estimates for a subset of solutions to irregular BSDEJs and subsequently proving the Tanaka-Krylov formula. Additionally, we employ a space transformation technique to simplify the initial BSDEJs, leading to a standard form without singular terms. We also provide various examples and special cases, shedding light on BSDEJs with irregular drift coefficients and contributing to new findings in the field.

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43

Gheorghiu, Călin-Ioan. "Accurate Spectral Collocation Computations of High Order Eigenvalues for Singular Schrödinger Equations-Revisited." Symmetry 13, no. 5 (April 27, 2021): 761. http://dx.doi.org/10.3390/sym13050761.

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In this paper, we continue to solve as accurately as possible singular eigenvalues problems attached to the Schrödinger equation. We use the conventional ChC and SiC as well as Chebfun. In order to quantify the accuracy of our outcomes, we use the drift with respect to some parameters, i.e., the order of approximation N, the length of integration interval X, or a small parameter ε, of a set of eigenvalues of interest. The deficiency of orthogonality of eigenvectors, which approximate eigenfunctions, is also an indication of the accuracy of the computations. The drift of eigenvalues provides an error estimation and, from that, one can achieve an error control. In both situations, conventional spectral collocation or Chebfun, the computing codes are simple and very efficient. An example for each such code is displayed so that it can be used. An extension to a 2D problem is also considered.

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44

Weber, Jan Erik H., and Kai H. Christensen. "On the singular behavior of the Stokes drift in layered miscible fluids." Wave Motion 102 (April 2021): 102712. http://dx.doi.org/10.1016/j.wavemoti.2021.102712.

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45

Zhang, Shao-Qin, and Chenggui Yuan. "A Zvonkin's transformation for stochastic differential equations with singular drift and applications." Journal of Differential Equations 297 (October 2021): 277–319. http://dx.doi.org/10.1016/j.jde.2021.06.031.

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46

Liu, Xuan, and Guangyu Xi. "On a maximal inequality and its application to SDEs with singular drift." Stochastic Processes and their Applications 130, no. 7 (July 2020): 4275–93. http://dx.doi.org/10.1016/j.spa.2019.12.004.

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47

Benguria, Rafael D., and Soledad Benguria. "The Brezis–Nirenberg problem for the Laplacian with a singular drift inRnandSn." Nonlinear Analysis 157 (July 2017): 189–211. http://dx.doi.org/10.1016/j.na.2017.03.006.

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48

Marinelli, Carlo, and Luca Scarpa. "A note on doubly nonlinear SPDEs with singular drift in divergence form." Rendiconti Lincei - Matematica e Applicazioni 29, no. 4 (December 28, 2018): 619–33. http://dx.doi.org/10.4171/rlm/825.

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49

Kim, Panki, and Renming Song. "Two-sided estimates on the density of Brownian motion with singular drift." Illinois Journal of Mathematics 50, no. 1-4 (2006): 635–88. http://dx.doi.org/10.1215/ijm/1258059487.

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50

Stummer, Wolfgang. "The Novikov and entropy conditions of multidimensional diffusion processes with singular drift." Probability Theory and Related Fields 97, no. 4 (December 1993): 515–42. http://dx.doi.org/10.1007/bf01192962.

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Journal articles on the topic 'Singular drift'

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