- formulasearchengine

General

Display information for equation id:math.225934.13 on revision:225934

* Page found: Geometric Brownian motion (eq math.225934.13)

Cannot find the equation data in the database. Fetching from revision text.

Occurrences on the following pages:

Hash: 5bffab625fac97a9aedea4573ffaf432

TeX (original user input):

\mathbb{E}(S_t)= S_0e^{\mu  t},

TeX (checked):

\mathbb {E} (S_{t})=S_{0}e^{\mu t},

LaTeXML (experimental; uses MathML) rendering

MathML (3.984 KB / 817 B) :

{\displaystyle{\mathbb{E}}(S_{t})=S_{0}e^{{\mu t}},}

<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\mathbb{E}}(S_{t})=S_{0}e^{{\mu t}},}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.12" xref="p1.1.m1.1.12.2.cmml">
      <mrow id="p1.1.m1.1.12.2" xref="p1.1.m1.1.12.2.cmml">
        <mrow id="p1.1.m1.1.12.2.1" xref="p1.1.m1.1.12.2.1.cmml">
          <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">𝔼</mi>
          <mo id="p1.1.m1.1.12.2.1.1" xref="p1.1.m1.1.12.2.1.1.cmml">⁢</mo>
          <mrow id="p1.1.m1.1.12.2.1.2" xref="p1.1.m1.1.12.2.1.2.2.cmml">
            <mo stretchy="false" id="p1.1.m1.1.2" xref="p1.1.m1.1.12.2.1.2.2.cmml">(</mo>
            <msub id="p1.1.m1.1.12.2.1.2.2" xref="p1.1.m1.1.12.2.1.2.2.cmml">
              <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">S</mi>
              <mi id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">t</mi>
            </msub>
            <mo stretchy="false" id="p1.1.m1.1.5" xref="p1.1.m1.1.12.2.1.2.2.cmml">)</mo>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">=</mo>
        <mrow id="p1.1.m1.1.12.2.2" xref="p1.1.m1.1.12.2.2.cmml">
          <msub id="p1.1.m1.1.12.2.2.2" xref="p1.1.m1.1.12.2.2.2.cmml">
            <mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">S</mi>
            <mn id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">0</mn>
          </msub>
          <mo id="p1.1.m1.1.12.2.2.1" xref="p1.1.m1.1.12.2.2.1.cmml">⁢</mo>
          <msup id="p1.1.m1.1.12.2.2.3" xref="p1.1.m1.1.12.2.2.3.cmml">
            <mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">e</mi>
            <mrow id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">
              <mi id="p1.1.m1.1.10.1.1" xref="p1.1.m1.1.10.1.1.cmml">μ</mi>
              <mo id="p1.1.m1.1.10.1.3" xref="p1.1.m1.1.10.1.3.cmml">⁢</mo>
              <mi id="p1.1.m1.1.10.1.2" xref="p1.1.m1.1.10.1.2.cmml">t</mi>
            </mrow>
          </msup>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.11" xref="p1.1.m1.1.12.2.cmml">,</mo>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.12.2.cmml" xref="p1.1.m1.1.12">
        <eq id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
        <apply id="p1.1.m1.1.12.2.1.cmml" xref="p1.1.m1.1.12.2.1">
          <times id="p1.1.m1.1.12.2.1.1.cmml" xref="p1.1.m1.1.12.2.1.1"/>
          <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝔼</ci>
          <apply id="p1.1.m1.1.12.2.1.2.2.cmml" xref="p1.1.m1.1.12.2.1.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.12.2.1.2.2.1.cmml" xref="p1.1.m1.1.12.2.1.2">subscript</csymbol>
            <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝑆</ci>
            <ci id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">𝑡</ci>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.12.2.2.cmml" xref="p1.1.m1.1.12.2.2">
          <times id="p1.1.m1.1.12.2.2.1.cmml" xref="p1.1.m1.1.12.2.2.1"/>
          <apply id="p1.1.m1.1.12.2.2.2.cmml" xref="p1.1.m1.1.12.2.2.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.12.2.2.2.1.cmml" xref="p1.1.m1.1.12.2.2.2">subscript</csymbol>
            <ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">𝑆</ci>
            <cn type="integer" id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">0</cn>
          </apply>
          <apply id="p1.1.m1.1.12.2.2.3.cmml" xref="p1.1.m1.1.12.2.2.3">
            <csymbol cd="ambiguous" id="p1.1.m1.1.12.2.2.3.1.cmml" xref="p1.1.m1.1.12.2.2.3">superscript</csymbol>
            <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">𝑒</ci>
            <apply id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">
              <times id="p1.1.m1.1.10.1.3.cmml" xref="p1.1.m1.1.10.1.3"/>
              <ci id="p1.1.m1.1.10.1.1.cmml" xref="p1.1.m1.1.10.1.1">𝜇</ci>
              <ci id="p1.1.m1.1.10.1.2.cmml" xref="p1.1.m1.1.10.1.2">𝑡</ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\mathbb{E}}(S_{t})=S_{0}e^{{\mu t}},}</annotation>
  </semantics>
</math>

SVG (7.647 KB / 3.014 KB) :

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

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :

PNG (0 B / 8 B) :

\mathbb {E} (S_{t})=S_{0}e^{\mu t},

Translations to Computer Algebra Systems

Translation to Maple

In Maple: E*(S[t])= S[0]*(e)^(mu*t),

Information about the conversion process:

e: the mathematical constant e == Napier's constant == 2.71828182845... was translated to: e

exp(1): You use a typical letter for a constant [the mathematical constant e == Napier's constant == 2.71828182845...].

We keep it like it is! But you should know that Maple uses exp(1) for this constant.

If you want to translate it as a constant, use the corresponding DLMF macro \expe

Translation to Mathematica

In Mathematica: E*(Subscript[S, t])= Subscript[S, 0]*(e)^(\[Mu]*t),

Information about the conversion process:

E: You use a typical letter for a constant [the mathematical constant e == Napier's constant == 2.71828182845...].

We keep it like it is! But you should know that Mathematica uses E for this constant.

If you want to translate it as a constant, use the corresponding DLMF macro \expe

e: the mathematical constant e == Napier's constant == 2.71828182845... was translated to: e

Identifiers

$\mathbb {E}$

$S_{t}$

$S_{0}$

$e$

$\mu$

$t$

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results