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Display information for equation id:math.225934.10 on revision:225934

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TeX (original user input):

d(\ln S_t) = \frac{d S_t}{S_t} -\frac{1}{2} \, \sigma^2 \, dt\,.

TeX (checked):

d(\ln S_{t})={\frac {dS_{t}}{S_{t}}}-{\frac {1}{2}}\,\sigma ^{2}\,dt\,.

LaTeXML (experimental; uses MathML) rendering

MathML (7.187 KB / 1.213 KB) :

d ( ln S t ) = d S t S t - 1 2 σ 2 d t . 𝑑 subscript 𝑆 𝑡 𝑑 subscript 𝑆 𝑡 subscript 𝑆 𝑡 1 2 superscript 𝜎 2 𝑑 𝑡 {\displaystyle d(\ln S_{t})={\frac{dS_{t}}{S_{t}}}-{\frac{1}{2}}\,\sigma^{2}\,% dt\,.}
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SVG (10.183 KB / 3.485 KB) :

d times left-parenthesis ln upper S Subscript t Baseline right-parenthesis equals StartFraction d times upper S Subscript t Baseline Over upper S Subscript t Baseline EndFraction minus one-half times sigma squared times d times t period

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MathML (0 B / 8 B) :

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Translations to Computer Algebra Systems

Translation to Maple

In Maple: d*(ln(S)[t])=(d*S[t])/(S[t])-(1)/(2)*(sigma)^(2)* d*t

Information about the conversion process:

\ln: Natural logarithm; Example: \ln@@{z}

Will be translated to: ln($0)

Constraints: z != 0

Branch Cuts: (-\infty, 0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.2#E2

Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=ln



Translation to Mathematica

In Mathematica: d*(Subscript[Log[S], t])=Divide[d*Subscript[S, t],Subscript[S, t]]-Divide[1,2]*\[Sigma]^(2)* d*t

Information about the conversion process:

\ln: Natural logarithm; Example: \ln@@{z}

Will be translated to: Log[$0]

Constraints: z != 0

Branch Cuts: (-\infty, 0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.2#E2

Mathematica: https://reference.wolfram.com/language/ref/Log.html



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