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[4 ] [5] Overfull \hbox (12.0844pt too wide) in paragraph at lines 182--183 []\OT1/cmr/m/it/10.95 A strong so-lu-tion to the stochas-tic dif-fer-en-tial eq ua-tion ([]1.1.5[]) on prob-a-bil-ity space $\OT1/cmr/m/n/10.95 ( \OML/cmm/m/it/10.95 ; \OMS/cmsy/m/n/10.95 F\OML/cmm/m/it/10.95 ; \U/msb/m/n/10. 95 P\OML/cmm/m/it/10.95 ; \OT1/cmr/m/n/10.95 (\U/msb/m/n/10.95 F[]\OT1/cmr/m/n/ 10.95 )[])$\OT1/cmr/m/it/10.95 , [] [6] [7] [8] LaTeX Font Info: Trying to load font information for U+BOONDOX-ds on input l ine 291. (/usr/local/texlive/2021/texmf-dist/tex/latex/boondox/uboondox-ds.fd File: uboondox-ds.fd 2011/04/26 Fontinst v1.933 font definitions for U/BOONDOX- ds. ) [9] Chapter 2. [10 ] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] Chapter 3. Package hyperref Warning: Token not allowed in a PDF string (Unicode): (hyperref) removing `math shift' on input line 749. 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[30] [31] [32] [33] Overfull \hbox (0.39136pt too wide) in paragraph at lines 1215--1218 []\OT1/cmr/m/n/10.95 However note also that since $\OML/cmm/m/it/10.95 G[]$ \OT 1/cmr/m/n/10.95 is up-per semi-continuous, fur-ther the fact that, $\OML/cmm/m/ it/10.95 ^^^[] \OMS/cmsy/m/n/10.95 2 []$\OT1/cmr/m/n/10.95 , [] Overfull \hbox (81.7409pt too wide) in paragraph at lines 1215--1218 \OT1/cmr/m/n/10.95 and then $([]3\OML/cmm/m/it/10.95 :\OT1/cmr/m/n/10.95 2\OML/ cmm/m/it/10.95 :\OT1/cmr/m/n/10.95 27[])$, and $([]3\OML/cmm/m/it/10.95 :\OT1/c mr/m/n/10.95 2\OML/cmm/m/it/10.95 :\OT1/cmr/m/n/10.95 16[])$, im-ply for all $\ OML/cmm/m/it/10.95 " \OMS/cmsy/m/n/10.95 2 \OT1/cmr/m/n/10.95 (0\OML/cmm/m/it/1 0.95 ; \OMS/cmsy/m/n/10.95 1\OT1/cmr/m/n/10.95 )$ we have that: $[][] [] = [] [34] [35] [36] [37] [38] [39] [40] [41] [42] Overfull \hbox (86.18391pt too wide) in paragraph at lines 1499--1500 \OT1/cmr/m/it/10.95 ery $\OML/cmm/m/it/10.95 r \OMS/cmsy/m/n/10.95 2 \OT1/cmr/m /n/10.95 (0\OML/cmm/m/it/10.95 ; \OMS/cmsy/m/n/10.95 1\OT1/cmr/m/n/10.95 )$ \OT 1/cmr/m/it/10.95 sat-isfy the con-di-tion that $\OML/cmm/m/it/10.95 O[] \OMS/cm sy/m/n/10.95 ^^R O$\OT1/cmr/m/it/10.95 , where $\OML/cmm/m/it/10.95 O[] \OT1/cm r/m/n/10.95 = \OMS/cmsy/m/n/10.95 f\OML/cmm/m/it/10.95 x \OMS/cmsy/m/n/10.95 2 O \OT1/cmr/m/n/10.95 : []\OMS/cmsy/m/n/10.95 g$ [] [43] [44] [45] [46] [47] Overfull \hbox (2.98135pt too wide) in paragraph at lines 1650--1651 []\OT1/cmr/bx/n/10.95 Corollary 3.3.1.1. []\OT1/cmr/m/it/10.95 Let $\OML/cmm/m/ it/10.95 T \OMS/cmsy/m/n/10.95 2 \OT1/cmr/m/n/10.95 (0\OML/cmm/m/it/10.95 ; \OM S/cmsy/m/n/10.95 1\OT1/cmr/m/n/10.95 )$\OT1/cmr/m/it/10.95 , let $[]$ be a prob -a-bil-ity space, let $\OML/cmm/m/it/10.95 u[] \OMS/cmsy/m/n/10.95 2 \OML/cmm/m /it/10.95 C[] []$\OT1/cmr/m/it/10.95 , [] [48] [49] ! Argument of \align has an extra }. \par l.1754 ...\|_F &= \| \mu(t,x) - \mu(t,y) \|_E+0} \nonumber\\ I've run across a `}' that doesn't seem to match anything. For example, `\def\a#1{...}' and `\a}' would produce this error. If you simply proceed now, the `\par' that I've just inserted will cause me to report a runaway argument that might be the root of the problem. But if your `}' was spurious, just type `2' and it will go away. Runaway argument? \| \mu (t,x) - \mu (t,y) \|_E+\|\sigma (t,x) - \sigma (t,y) \|_F &= \ETC. ! Paragraph ended before \align was complete. \par l.1754 ...\|_F &= \| \mu(t,x) - \mu(t,y) \|_E+0} \nonumber\\ I suspect you've forgotten a `}', causing me to apply this control sequence to too much text. How can we recover? My plan is to forget the whole thing and hope for the best. ! Missing $ inserted. $ l.1754 ...\|_F &= \| \mu(t,x) - \mu(t,y) \|_E+0} \nonumber\\ I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing } inserted. } l.1754 ...\|_F &= \| \mu(t,x) - \mu(t,y) \|_E+0} \nonumber\\ I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing \endgroup inserted. \endgroup l.1754 ...\|_F &= \| \mu(t,x) - \mu(t,y) \|_E+0} \nonumber\\ I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Display math should end with $$. \@@par l.1754 ...\|_F &= \| \mu(t,x) - \mu(t,y) \|_E+0} \nonumber\\ The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Extra }, or forgotten \endgroup. \par ...m \@noitemerr {\@@par }\fi \else {\@@par } \fi l.1754 ...\|_F &= \| \mu(t,x) - \mu(t,y) \|_E+0} \nonumber\\ I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Extra }, or forgotten \endgroup. } l.1754 ...\|_F &= \| \mu(t,x) - \mu(t,y) \|_E+0} \nonumber\\ I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! LaTeX Error: There's no line here to end. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.1755 & = \|t\nabla_x\alpha(x) - t\nabla_x \alpha(y) \|_E} \nonumber\\ Your command was ignored. Type I to replace it with another command, or to continue without it. ! Misplaced alignment tab character &. & l.1755 & = \|t\nabla_x\alpha(x) - t\nabla_x \alpha(y) \|_E} \nonumber\\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Missing $ inserted. $ l.1755 &= \| t\nabla_x\alpha(x) - t\nabla_x \alpha(y) \|_E} \nonumber\\ I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.1755 ...a_x\alpha(x) - t\nabla_x \alpha(y) \|_E} \nonumber\\ I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Misplaced alignment tab character &. & l.1756 & \leq \frac{T\|\nabla_x\alpha(x)-\nabla_x\alpha(y)\|_E}{\lp \|x\|_E ... I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. & l.1757 & \leq 2T\mathfrak{B} \leq I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced \cr. \math@cr@@@ ->\cr l.1758 \end{align} I can't figure out why you would want to use a tab mark or \cr or \span just now. If something like a right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced \noalign. \math@cr@@ ... \iffalse }\fi \math@cr@@@ \noalign {\vskip #1\relax } l.1758 \end{align} I expect to see \noalign only after the \cr of an alignment. Proceed, and I'll ignore this case. ! Missing $ inserted. $ l.1758 \end{align} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing } inserted. } l.1758 \end{align} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Extra }, or forgotten \endgroup. \math@cr@@ ...th@cr@@@ \noalign {\vskip #1\relax } l.1758 \end{align} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Misplaced \noalign. \black@ #1->\noalign {\ifdim #1>\displaywidth \dimen@ \prevdepth \nointerlin... l.1758 \end{align} I expect to see \noalign only after the \cr of an alignment. Proceed, and I'll ignore this case. Overfull \hbox (259.72743pt too wide) detected at line 1758 [] [] ! Extra }, or forgotten \endgroup. \endalign ->\math@cr \black@ \totwidth@ \egroup \ifingather@ \restorealignst... l.1758 \end{align} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.1758 \end{align} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Display math should end with $$. \endgroup l.1758 \end{align} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. [50] [51] [52] (./Dissertation.bbl [53 ]) [54] [55 ] [56] (./Dissertation.aux) LaTeX Warning: There were undefined references. LaTeX Warning: There were multiply-defined labels. Package rerunfilecheck Info: File `Dissertation.out' has not changed. (rerunfilecheck) Checksum: EA82F68FD5620E41892B53C13EE56636;2174. ) (\end occurred inside a group at level 1) ### simple group (level 1) entered at line 91 ({) ### bottom level Here is how much of TeX's memory you used: 12969 strings out of 478994 199090 string characters out of 5858184 532732 words of memory out of 5000000 29889 multiletter control sequences out of 15000+600000 421865 words of font info for 102 fonts, out of 8000000 for 9000 1141 hyphenation exceptions out of 8191 71i,18n,74p,917b,628s stack positions out of 5000i,500n,10000p,200000b,80000s Output written on Dissertation.pdf (58 pages, 406328 bytes). PDF statistics: 984 PDF objects out of 1000 (max. 8388607) 893 compressed objects within 9 object streams 392 named destinations out of 1000 (max. 500000) 89 words of extra memory for PDF output out of 10000 (max. 10000000)