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010 a| 2022007685;

020 a| 9781470450007q| (paperback);

020 z| 9781470468095q| (epub);

035 a| (WaSeSS)ssj0002594502;

042 a| pcc;

049 a| EREEa| NEHH;

050 00 a| QA377b| .C4388 2021;

082 00 a| 519.2/22| 23/eng20220502;

084 a| 60H15a| 60G60a| 35R602| msc;

100 1 a| Chen, Le,d| 1979-?| UNAUTHORIZED;

245 10 a| Regularity and strict positivity of densities for the nonlinear stochastic heat equationsh| [electronic resource] /c| Le Chen, Yaozhong Hu, David Nualart.;

260 a| Providence :b| American Mathematical Society,c| [2021];

300 a| v, 102 pages :b| illustrations ;c| 26 cm;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| Volume 273, Number 1340 (third of 5 numbers);

504 a| IIncludes bibliographical references (pages 101-102).;

506 a| Available only to authorized users.;

520 a| "In this paper, we establish a necessary and sufficient condition for the existence and regularity of the density of the solution to a semilinear stochastic (fractional) heat equation with measure-valued initial conditions. Under a mild cone condition for the diffusion coefficient, we establish the smooth joint density at multiple points. The tool we use is Malliavin calculus. The main ingredient is to prove that the solutions to a related stochastic partial differential equation have negative moments of all orders. Because we cannot prove u(t, x) D for measure-valued initial data, we need a localized version of Malliavin calculus. Furthermore, we prove that the (joint) density is strictly positive in the interior of the support of the law, where we allow both measure-valued initial data and unbounded diffusion coefficient. The criteria introduced by Bally and Pardoux are no longer applicable for the parabolic Anderson model. We have extended their criteria to a localized version. Our general framework includes the parabolic Anderson model as a special case"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Heat equation.=| ^A68539;

650 0 a| Stochastic partial differential equations.=| ^A269969;

650 0 a| Nonlinear difference equations.=| ^A572449;

650 0 a| Malliavin calculus.=| ^A286905;

650 7 a| Probability theory and stochastic processes -- Stochastic analysis -- Stochastic partial differential equations.2| msc;

650 7 a| Probability theory and stochastic processes -- Stochastic processes -- Random fields.2| msc;

650 7 a| Partial differential equations -- Miscellaneous topics -- Partial differential equations with randomness, stochastic partial differential equations.2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Hu, Yaozhong,d| 1961-=| ^A595573;

700 1 a| Nualart, David,d| 1951-=| ^A363862;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=6822188;

949 a| CLICK ON WEB ADDRESSw| ASISh| JOYNER188;

949 a| CLICK ON WEB ADDRESSw| ASISh| HSL77;

949 a| CLICK ON WEB ADDRESSw| ASISh| JMUSIC60;

596 a| 1 3 4;

998 a| 6515981;

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999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6515981-2001l| HSLELECm| HSLr| Ys| Yt| HEBKu| 1/14/2025x| EBOOKz| HERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6515981-3001l| MNETm| JMUSICr| Ys| Yt| MNESSBKu| 1/14/2025x| EBOOKz| JERESOURCE;

Regularity and strict positivity of densities for the nonlinear stochastic heat equations / Le Chen, Yaozhong Hu, David Nualart.

Author/creator	Chen, Le, 1979-
Other author	Hu, Yaozhong, 1961-
Other author	Nualart, David, 1951-
Format	Electronic
Publication Info	Providence : American Mathematical Society, [2021]
Description	v, 102 pages : illustrations ; 26 cm
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Heat equation. Stochastic partial differential equations. Nonlinear difference equations. Malliavin calculus.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; Volume 273, Number 1340 (third of 5 numbers)
Abstract	"In this paper, we establish a necessary and sufficient condition for the existence and regularity of the density of the solution to a semilinear stochastic (fractional) heat equation with measure-valued initial conditions. Under a mild cone condition for the diffusion coefficient, we establish the smooth joint density at multiple points. The tool we use is Malliavin calculus. The main ingredient is to prove that the solutions to a related stochastic partial differential equation have negative moments of all orders. Because we cannot prove u(t, x) D for measure-valued initial data, we need a localized version of Malliavin calculus. Furthermore, we prove that the (joint) density is strictly positive in the interior of the support of the law, where we allow both measure-valued initial data and unbounded diffusion coefficient. The criteria introduced by Bally and Pardoux are no longer applicable for the parabolic Anderson model. We have extended their criteria to a localized version. Our general framework includes the parabolic Anderson model as a special case"-- Provided by publisher.
Bibliography note	IIncludes bibliographical references (pages 101-102).
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2022007685
ISBN	9781470450007 (paperback)
ISBN	(epub)

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Regularity and strict positivity of densities for the nonlinear stochastic heat equations / Le Chen, Yaozhong Hu, David Nualart.

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