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Display information for equation id:math.225934.11 on revision:225934

* Page found: Geometric Brownian motion (eq math.225934.11)

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TeX (original user input):

\ln \frac{S_t}{S_0} = \left(\mu -\frac{\sigma^2}{2}\,\right) t + \sigma W_t\,.

TeX (checked):

\ln {\frac {S_{t}}{S_{0}}}=\left(\mu -{\frac {\sigma ^{2}}{2}}\,\right)t+\sigma W_{t}\,.

LaTeXML (experimental; uses MathML) rendering

MathML (6.666 KB / 1.157 KB) :

ln S t S 0 = ( μ - σ 2 2 ) t + σ W t . subscript 𝑆 𝑡 subscript 𝑆 0 𝜇 superscript 𝜎 2 2 𝑡 𝜎 subscript 𝑊 𝑡 {\displaystyle\ln{\frac{S_{t}}{S_{0}}}=\left(\mu-{\frac{\sigma^{2}}{2}}\,% \right)t+\sigma W_{t}\,.}
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SVG (11.87 KB / 4.396 KB) :

ln StartFraction upper S Subscript t Baseline Over upper S 0 EndFraction equals left-parenthesis mu minus StartFraction sigma squared Over 2 EndFraction right-parenthesis times t plus sigma times upper W Subscript t Baseline period

MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools) rendering

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Translations to Computer Algebra Systems

Translation to Maple

In Maple: ln((S[t])/(S[0]))=(mu -((sigma)^(2))/(2))* t + sigma*W[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: Log[Divide[Subscript[S, t],Subscript[S, 0]]]=(\[Mu]-Divide[\[Sigma]^(2),2])* t + \[Sigma]*Subscript[W, 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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