PATHWISE UNIQUENESS OF THE STOCHASTIC HEAT EQUATION WITH SPATIALLY INHOMOGENEOUS WHITE NOISE

被引：8
作者：
Neuman, Eyal [1 ]
机构：
[1] Imperial Coll London, London SW7 2AZ, England
来源：
ANNALS OF PROBABILITY | 2018年 / 46卷 / 06期
关键词：
Uniqueness; white noise; stochastic partial differential equations; heat equation; catalytic superprocesses; PARTIAL-DIFFERENTIAL-EQUATIONS; NONUNIQUENESS; COEFFICIENTS;
D O I：
10.1214/17-AOP1239
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We study the solutions of the stochastic heat equation driven by spatially inhomogeneous multiplicative white noise based on a fractal measure. We prove pathwise uniqueness for solutions of this equation when the noise co-efficient is Holder continuous of index gamma > 1 - eta/2(eta+1). Here eta is an element of (0, 1) is a constant that defines the spatial regularity of the noise.
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收藏
页码：3090 / 3187
页数：98
相关论文
共 25 条
  • [1] [Anonymous], 2002, Lecture Notes in Mathematics
  • [2] [Anonymous], INFINITE DIMENSIONAL
  • [3] NONUNIQUENESS FOR NONNEGATIVE SOLUTIONS OF PARABOLIC STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
    Burdzy, K.
    Mueller, C.
    Perkins, E. A.
    [J]. ILLINOIS JOURNAL OF MATHEMATICS, 2010, 54 (04) : 1481 - 1507
  • [4] VIBRATING STRING FORCED BY WHITE NOISE
    CABANA, EM
    [J]. ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1970, 15 (02): : 111 - &
  • [5] PATHWISE NONUNIQUENESS FOR THE SPDES OF SOME SUPER-BROWNIAN MOTIONS WITH IMMIGRATION
    Chen, Yu-Ting
    [J]. ANNALS OF PROBABILITY, 2015, 43 (06) : 3359 - 3467
  • [6] Da Prato G., 1987, Stochastics, V23, P1, DOI 10.1080/17442508708833480
  • [7] DAWSON D A, 1972, Mathematical Biosciences, V15, P287, DOI 10.1016/0025-5564(72)90039-9
  • [8] Dawson D.A., 1975, J. Multivar. Anal, V5, P1, DOI 10.1016/0047-259X(75)90054-8
  • [9] Falconer KJ., 2003, FRACTAL GEOMETRY MAT, DOI 10.1002/0470013850
  • [10] FUNAKI T., 1984, STOCHASTIC ANAL, V32, P121
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