%PDF-1.5 % 4 0 obj << /S /GoTo /D (section.1) >> endobj 7 0 obj (1. Introduction) endobj 8 0 obj << /S /GoTo /D (subsection.1.1) >> endobj 11 0 obj (1.1. Main results) endobj 12 0 obj << /S /GoTo /D (subsection.1.2) >> endobj 15 0 obj (1.2. Sketch of proofs and structure of the paper) endobj 16 0 obj << /S /GoTo /D (subsection.1.3) >> endobj 19 0 obj (1.3. Conventions and notations) endobj 20 0 obj << /S /GoTo /D (section.2) >> endobj 23 0 obj (2. Preliminaries) endobj 24 0 obj << /S /GoTo /D (subsection.2.1) >> endobj 27 0 obj (2.1. Weighted Besov spaces) endobj 28 0 obj << /S /GoTo /D (subsection.2.2) >> endobj 31 0 obj (2.2. Estimates of Gaussian heat semigroups) endobj 32 0 obj << /S /GoTo /D (subsection.2.3) >> endobj 35 0 obj (2.3. Paracontrolled calculus) endobj 36 0 obj << /S /GoTo /D (subsection.2.4) >> endobj 39 0 obj (2.4. Renormalized pairs) endobj 40 0 obj << /S /GoTo /D (section.3) >> endobj 43 0 obj (3. A study of linear parabolic equation in weighted H\366lder spaces) endobj 44 0 obj << /S /GoTo /D (subsection.3.1) >> endobj 47 0 obj (3.1. Paracontrolled solutions) endobj 48 0 obj << /S /GoTo /D (subsection.3.2) >> endobj 51 0 obj (3.2. Schauder's estimate for paracontrolled solutions without weights) endobj 52 0 obj << /S /GoTo /D (subsection.3.3) >> endobj 55 0 obj (3.3. Schauder estimate for paracontrolled solutions with weights) endobj 56 0 obj << /S /GoTo /D (section.4) >> endobj 59 0 obj (4. Hamilton-Jacobi-Bellman equations) endobj 60 0 obj << /S /GoTo /D (subsection.4.1) >> endobj 63 0 obj (4.1. Maximum principle in weighted spaces) endobj 64 0 obj << /S /GoTo /D (subsection.4.2) >> endobj 67 0 obj (4.2. Subcritical case) endobj 68 0 obj << /S /GoTo /D (subsection.4.3) >> endobj 71 0 obj (4.3. Critical one dimensional case) endobj 72 0 obj << /S /GoTo /D (subsection.4.4) >> endobj 75 0 obj (4.4. Proof of Theorem 4.2) endobj 76 0 obj << /S /GoTo /D (section.5) >> endobj 79 0 obj (5. HJB equations with distribution-valued coefficients) endobj 80 0 obj << /S /GoTo /D (subsection.5.1) >> endobj 83 0 obj (5.1. Zvonkin's transformation for HJB equations) endobj 84 0 obj << /S /GoTo /D (subsection.5.2) >> endobj 87 0 obj (5.2. Proof of Theorem 5.1) endobj 88 0 obj << /S /GoTo /D (section.6) >> endobj 91 0 obj (6. Application to KPZ equations) endobj 92 0 obj << /S /GoTo /D (appendix.A) >> endobj 95 0 obj (Appendix A. Uniqueness of paracontrolled solutions) endobj 96 0 obj << /S /GoTo /D (appendix.B) >> endobj 99 0 obj (Appendix B. Exponential moment estimates for SDEs) endobj 100 0 obj << /S /GoTo /D (section*.2) >> endobj 103 0 obj (Acknowlegement) endobj 104 0 obj << /S /GoTo /D (section*.3) >> endobj 107 0 obj (References) endobj 108 0 obj << /S /GoTo /D [109 0 R /Fit] >> endobj 140 0 obj << /Length 2041 /Filter /FlateDecode >> stream xڭXKs6Whb|'qmʴ4-6ǽwRԫagz" v}ΓÝdnx3tnN(7Tҙ/d]9A}?_߮4ܼ:y8?Gߟo'o!+ș *"qst{>{KWqOq1 "WpL؍"T_@`Dr|qfa{;7~M߯f;+-]#ndy,mܝ[*(߅v͗Y N&A>g"MlL^)iAݴxԥ&e,o|Ȧ:WIa3%S\n&+!{Κ%=892c-b 8R4rc"H3] ʦF=/ KZYEX98 Ȧܯ b "#iu&9 j]ԨuYR,,mvтXnsi,mM BXM#2ϵ8J7^=ԍX6fBq9pzrhp{q.nX@c/'!6~5[i/g)i)!{Zʦsė+s0ujbvOAZ|ʊW5 !VV.F9vf%Jf-*9]70kҀ؏Jx `Wg5DDt/8xp/HuM0i"8d^MM .ÀlIwvtD`5@8l8eAd+AJ0c*m*\ef & 'C1:IۃulV^k0fCߊ;SM C]m;+FMmCUO nGSItXZp+fzޕAB*dyn/)Uyy9B15quE** km)k"TAа0ܙN*&C`~