Jump to navigation Jump to search

General

Display information for equation id:math.225934.21 on revision:225934

* Page found: Geometric Brownian motion (eq math.225934.21)

(force rerendering)

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

Occurrences on the following pages:

Hash: 100fcc6bc41ec6c7aa42bc8a6129fa8f

TeX (original user input): 

 \mathbb{E}(dW_{t}^i dW_{t}^j) = \rho_{i,j} dt

TeX (checked): 

\mathbb {E} (dW_{t}^{i}dW_{t}^{j})=\rho _{i,j}dt

LaTeXML (experimental; uses MathML) rendering

MathML (5.59 KB / 966 B) :

𝔼 ⁢ ( d ⁢ W t i ⁢ d ⁢ W t j ) = ρ i , j ⁢ d ⁢ t 𝔼 𝑑 superscript subscript 𝑊 𝑡 𝑖 𝑑 superscript subscript 𝑊 𝑡 𝑗 subscript 𝜌 𝑖 𝑗 𝑑 𝑡 {\displaystyle{\mathbb{E}}(dW_{{t}}^{i}dW_{{t}}^{j})=\rho_{{i,j}}dt} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\mathbb{E}}(dW_{{t}}^{i}dW_{{t}}^{j})=\rho_{{i,j}}dt}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">
      <mrow id="p1.1.m1.1.17.1" xref="p1.1.m1.1.17.1.cmml">
        <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">𝔼</mi>
        <mo id="p1.1.m1.1.17.1.1" xref="p1.1.m1.1.17.1.1.cmml">⁢</mo>
        <mrow id="p1.1.m1.1.17.1.2" xref="p1.1.m1.1.17.1.2.2.cmml">
          <mo stretchy="false" id="p1.1.m1.1.2" xref="p1.1.m1.1.17.1.2.2.cmml">(</mo>
          <mrow id="p1.1.m1.1.17.1.2.2" xref="p1.1.m1.1.17.1.2.2.cmml">
            <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">d</mi>
            <mo id="p1.1.m1.1.17.1.2.2.1" xref="p1.1.m1.1.17.1.2.2.1.cmml">⁢</mo>
            <msubsup id="p1.1.m1.1.17.1.2.2.2" xref="p1.1.m1.1.17.1.2.2.2.cmml">
              <mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">W</mi>
              <mi id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">t</mi>
              <mi id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">i</mi>
            </msubsup>
            <mo id="p1.1.m1.1.17.1.2.2.1a" xref="p1.1.m1.1.17.1.2.2.1.cmml">⁢</mo>
            <mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">d</mi>
            <mo id="p1.1.m1.1.17.1.2.2.1b" xref="p1.1.m1.1.17.1.2.2.1.cmml">⁢</mo>
            <msubsup id="p1.1.m1.1.17.1.2.2.3" xref="p1.1.m1.1.17.1.2.2.3.cmml">
              <mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">W</mi>
              <mi id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">t</mi>
              <mi id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">j</mi>
            </msubsup>
          </mrow>
          <mo stretchy="false" id="p1.1.m1.1.11" xref="p1.1.m1.1.17.1.2.2.cmml">)</mo>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">=</mo>
      <mrow id="p1.1.m1.1.17.2" xref="p1.1.m1.1.17.2.cmml">
        <msub id="p1.1.m1.1.17.2.2" xref="p1.1.m1.1.17.2.2.cmml">
          <mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">ρ</mi>
          <mrow id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.4.cmml">
            <mi id="p1.1.m1.1.14.1.1" xref="p1.1.m1.1.14.1.1.cmml">i</mi>
            <mo id="p1.1.m1.1.14.1.2" xref="p1.1.m1.1.14.1.4.cmml">,</mo>
            <mi id="p1.1.m1.1.14.1.3" xref="p1.1.m1.1.14.1.3.cmml">j</mi>
          </mrow>
        </msub>
        <mo id="p1.1.m1.1.17.2.1" xref="p1.1.m1.1.17.2.1.cmml">⁢</mo>
        <mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">d</mi>
        <mo id="p1.1.m1.1.17.2.1a" xref="p1.1.m1.1.17.2.1.cmml">⁢</mo>
        <mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">t</mi>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">
        <eq id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12"/>
        <apply id="p1.1.m1.1.17.1.cmml" xref="p1.1.m1.1.17.1">
          <times id="p1.1.m1.1.17.1.1.cmml" xref="p1.1.m1.1.17.1.1"/>
          <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝔼</ci>
          <apply id="p1.1.m1.1.17.1.2.2.cmml" xref="p1.1.m1.1.17.1.2">
            <times id="p1.1.m1.1.17.1.2.2.1.cmml" xref="p1.1.m1.1.17.1.2.2.1"/>
            <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝑑</ci>
            <apply id="p1.1.m1.1.17.1.2.2.2.cmml" xref="p1.1.m1.1.17.1.2.2.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.17.1.2.2.2.1.cmml" xref="p1.1.m1.1.17.1.2.2.2">superscript</csymbol>
              <apply id="p1.1.m1.1.17.1.2.2.2.2.cmml" xref="p1.1.m1.1.17.1.2.2.2">
                <csymbol cd="ambiguous" id="p1.1.m1.1.17.1.2.2.2.2.1.cmml" xref="p1.1.m1.1.17.1.2.2.2">subscript</csymbol>
                <ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">𝑊</ci>
                <ci id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">𝑡</ci>
              </apply>
              <ci id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">𝑖</ci>
            </apply>
            <ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">𝑑</ci>
            <apply id="p1.1.m1.1.17.1.2.2.3.cmml" xref="p1.1.m1.1.17.1.2.2.3">
              <csymbol cd="ambiguous" id="p1.1.m1.1.17.1.2.2.3.1.cmml" xref="p1.1.m1.1.17.1.2.2.3">superscript</csymbol>
              <apply id="p1.1.m1.1.17.1.2.2.3.2.cmml" xref="p1.1.m1.1.17.1.2.2.3">
                <csymbol cd="ambiguous" id="p1.1.m1.1.17.1.2.2.3.2.1.cmml" xref="p1.1.m1.1.17.1.2.2.3">subscript</csymbol>
                <ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">𝑊</ci>
                <ci id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">𝑡</ci>
              </apply>
              <ci id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">𝑗</ci>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.17.2.cmml" xref="p1.1.m1.1.17.2">
          <times id="p1.1.m1.1.17.2.1.cmml" xref="p1.1.m1.1.17.2.1"/>
          <apply id="p1.1.m1.1.17.2.2.cmml" xref="p1.1.m1.1.17.2.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.17.2.2.1.cmml" xref="p1.1.m1.1.17.2.2">subscript</csymbol>
            <ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">𝜌</ci>
            <list id="p1.1.m1.1.14.1.4.cmml" xref="p1.1.m1.1.14.1">
              <ci id="p1.1.m1.1.14.1.1.cmml" xref="p1.1.m1.1.14.1.1">𝑖</ci>
              <ci id="p1.1.m1.1.14.1.3.cmml" xref="p1.1.m1.1.14.1.3">𝑗</ci>
            </list>
          </apply>
          <ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">𝑑</ci>
          <ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">𝑡</ci>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\mathbb{E}}(dW_{{t}}^{i}dW_{{t}}^{j})=\rho_{{i,j}}dt}</annotation>
  </semantics>
</math>

SVG (9.719 KB / 3.609 KB) :

double-struck upper E times left-parenthesis d times upper W Subscript t Superscript i Baseline times d times upper W Subscript t Superscript j Baseline right-parenthesis equals rho Subscript i comma j Baseline times d times t

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) :


Translations to Computer Algebra Systems

Translation to Maple

In Maple: (d*W(W[t])^(i)*d*W(W[t])^(j))= rho[i , j]*d*t

Information about the conversion process:

I: You use a typical letter for a constant [the imaginary unit == the principal square root of -1].

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

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


i: the imaginary unit == the principal square root of -1 was translated to: i


Translation to Mathematica

In Mathematica: (d*W(Subscript[W, t])^(i)*d*W(Subscript[W, t])^(j))= Subscript[\[Rho], i , j]*d*t

Information about the conversion process:

I: You use a typical letter for a constant [the imaginary unit == the principal square root of -1].

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

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


i: the imaginary unit == the principal square root of -1 was translated to: i


Similar pages

Calculated based on the variables occurring on the entire Geometric Brownian motion page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results

Retrieved from "https://en.formulasearchengine.com/wiki/Special:FormulaInfo"