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Display information for equation id:math.225934.17 on revision:225934

* Page found: Geometric Brownian motion (eq math.225934.17)

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TeX (original user input):

\mathbb{E} \log(S_t)=\log(S_0)+(\mu-\sigma^2/2)t

TeX (checked):

\mathbb {E} \log(S_{t})=\log(S_{0})+(\mu -\sigma ^{2}/2)t

LaTeXML (experimental; uses MathML) rendering

MathML (6.162 KB / 1.066 KB) :

𝔼 log ( S t ) = log ( S 0 ) + ( μ - σ 2 / 2 ) t 𝔼 subscript 𝑆 𝑡 subscript 𝑆 0 𝜇 superscript 𝜎 2 2 𝑡 {\displaystyle{\mathbb{E}}\log(S_{t})=\log(S_{0})+(\mu-\sigma^{2}/2)t}
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SVG (11.801 KB / 4.256 KB) :

double-struck upper E times log left-parenthesis upper S Subscript t Baseline right-parenthesis equals log left-parenthesis upper S 0 right-parenthesis plus left-parenthesis mu minus sigma squared slash 2 right-parenthesis times t

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Translations to Computer Algebra Systems

Translation to Maple

In Maple: E*log(S[t])= log(S[0])+(mu - (sigma)^(2)/ 2)* t

Information about the conversion process:

\log: Logarithm; Example: \log@@{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

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



Translation to Mathematica

In Mathematica: E*Log[Subscript[S, t]]= Log[Subscript[S, 0]]+(\[Mu]- \[Sigma]^(2)/ 2)* t

Information about the conversion process:

\log: Logarithm; Example: \log@@{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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