Ito calculus - 편집 역사

Pythagoras0: /* 메타데이터 */

2022-08-22T03:13:16Z

메타데이터

Pythagoras0: /* 메타데이터 */ 새 문단

2022-08-22T03:07:10Z

메타데이터: 새 문단

Pythagoras0: /* 노트 */ 새 문단

2022-08-22T03:07:08Z

노트: 새 문단

2021년 2월 17일 (수) 10:09에 Pythagoras0님의 편집

2021-02-17T10:09:23Z

2020년 12월 28일 (월) 12:06에 Pythagoras0님의 편집

2020-12-28T12:06:04Z

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-28T08:26:23Z

메타데이터: 새 문단

2020년 11월 16일 (월) 12:26에 Pythagoras0님의 편집

2020-11-16T12:26:44Z

2020년 11월 13일 (금) 07:24에 imported>Pythagoras0님의 편집

2020-11-13T07:24:32Z

imported>Pythagoras0: /* basic probability theory */

2016-06-09T03:02:46Z

basic probability theory

imported>Pythagoras0: /* computational resource */

2016-06-09T02:55:50Z

computational resource

@@ 56번째 줄: / 56번째 줄: @@
 [[분류:probability]]
 [[분류:migrate]]
 == 노트 ==

← 이전 판		2022년 8월 22일 (월) 03:07 판
75번째 줄:		75번째 줄:
	===소스===		===소스===
	<references />		<references />
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q947053 Q947053]
		+	===Spacy 패턴 목록===
		+	* [{'LOWER': 'ito'}, {'LEMMA': 'calculus'}]
		+	* [{'LOWER': 'itō'}, {'LEMMA': 'calculus'}]

← 이전 판		2022년 8월 22일 (월) 03:07 판
62번째 줄:		62번째 줄:
	===Spacy 패턴 목록===		===Spacy 패턴 목록===
	* [{'LOWER': 'itō'}, {'LEMMA': 'calculus'}]		* [{'LOWER': 'itō'}, {'LEMMA': 'calculus'}]
		+
		+	== 노트 ==
		+
		+	===말뭉치===
		+	# Vlad Gheorghiu (CMU) Ito calculus in a nutshell April 7, 2011 4 / 23 Elementary random processes If we now calculate expectations of Si it does matter what information we have.<ref name="ref_680e2caa">[https://quantum.phys.cmu.edu/QIP/ito_calculus.pdf Itˆo calculus in a nutshell]</ref>
		+	# Itos lemma is often used in Ito calculus to nd the dierentials of a stochastic process that depends on time.<ref name="ref_1f963234">[https://math.uchicago.edu/~may/REU2017/REUPapers/Yoo.pdf Stochastic calculus and black-scholes model]</ref>
		+	# The Ito calculus is about systems driven by white noise.<ref name="ref_fc563a79">[https://www.math.nyu.edu/~goodman/teaching/StochCalc2007/notes/l7.pdf Stochastic calculus notes, lecture 7]</ref>
		+	# This test of survival under the limit dt=0 and sum determines the rules ( Ito calculus ) at the beginning of this section.<ref name="ref_458abe97">[http://www.lukoe.com/finance/quantNotes/Ito_calculus_.html Ito calculus.]</ref>
		+	# 1. First Contact with Ito Calculus From the practitioners point of view, the Ito calculus is a tool for manip- ulating those stochastic processes which are most closely related to Brow- nian motion.<ref name="ref_507f2020">[http://www-stat.wharton.upenn.edu/~steele/Publications/PDF/EASItoCalculus.pdf It ˆo calculus]</ref>
		+	# Abstract The Functional Ito calculus is a non-anticipative functional calculus which extends the Ito calculus to path-dependent functionals of stochas- tic processes.<ref name="ref_6196a20d">[http://rama.cont.perso.math.cnrs.fr/BarcelonaLectureNotes.pdf Functional ito calculus]</ref>
		+	# The Functional Ito calculus has led to various applications in the study of path-dependent functionals of stochastic processes.<ref name="ref_6196a20d" />
		+	===소스===
		+	<references />

@@ 57번째 줄: / 57번째 줄: @@
 [[분류:migrate]]
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
 * ID :  [https://www.wikidata.org/wiki/Q947053 Q947053]

@@ 40번째 줄: / 40번째 줄: @@
 * Loewner equantion
-−
 ==related items==

← 이전 판		2020년 12월 28일 (월) 08:26 판
56번째 줄:		56번째 줄:
	[[분류:probability]]		[[분류:probability]]
	[[분류:migrate]]		[[분류:migrate]]
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q947053 Q947053]

@@ 10번째 줄: / 10번째 줄: @@
 ==Ito SDE==
 ;def
-A stochastic process $X(t)$ is said to satisfy an Ito SDE, written as,
+A stochastic process <math>X(t)</math> is said to satisfy an Ito SDE, written as,
-$$
+:<math>
 dX(t)= \alpha(X(t),t)dt+\beta(X(t),t)dW(t)\label{ito}
-$$
+</math>
-if for $t\ge 0$ it satisfies the integral equation,
+if for <math>t\ge 0</math> it satisfies the integral equation,
-$$
+:<math>
 X(t)= X(0) +\int_{0}^{t}\alpha(X(\tau),\tau)\,d\tau+\int_{0}^{t}\beta(X(\tau),\tau)dW(\tau)
-$$
+</math>
 ===Kolmogorov equation===
 * [[Fokker-Planck equation|Fokker-Planck equations]], also known as Fokker-Planck-Kolmogorov equations or forward Kolmogorov equations, are deterministic equations describing how probability density functions evolve
-* let $p(x,t)$ be the p.d.f. of the stochastic process $X(t)$ satisfying \ref{ito}. Then
+* let <math>p(x,t)</math> be the p.d.f. of the stochastic process <math>X(t)</math> satisfying \ref{ito}. Then
-$$
+:<math>
 \frac{\partial p}{\partial t} = -\frac{\partial(\alpha(x,t)p)}{\partial x}+\frac{1}{2}\frac{\partial^2 (\beta^2(x,t)p)}{\partial x^2}
-$$
+</math>
 ===multi-dimensional version===
 * see Klebaner2005
@@ 30번째 줄: / 30번째 줄: @@
    {\rm d} X(t) = f(X(t)){\rm d}t + \sigma(X(t))  {\rm d} B(t), \qquad  X(0) = x_0\in \mathbb{R}^{d},
 \end{equation}
-where $X(t)=(X_1(t),X_2(t),\cdots,X_d(t))^T \in \mathbb{R}^d$, $f=(f_1, f_2,\cdots,f_d)^T: \mathbb{R}^d\to \mathbb{R}^d$, $\sigma=(\sigma_{ij})_{d\times n}: \mathbb{R}^d \to \mathbb{R}^{d\times n}$. $B(t)$ is an $n$-dimensional Brownian motion,  and $f$ and $g$ satisfy certain smoothness conditions.    The probability density function $p(x,t)$ for the solution $X(t)$ in (\ref{s1_000}) can be expressed as
+where <math>X(t)=(X_1(t),X_2(t),\cdots,X_d(t))^T \in \mathbb{R}^d</math>, <math>f=(f_1, f_2,\cdots,f_d)^T: \mathbb{R}^d\to \mathbb{R}^d</math>, <math>\sigma=(\sigma_{ij})_{d\times n}: \mathbb{R}^d \to \mathbb{R}^{d\times n}</math>. <math>B(t)</math> is an <math>n</math>-dimensional Brownian motion,  and <math>f</math> and <math>g</math> satisfy certain smoothness conditions.    The probability density function <math>p(x,t)</math> for the solution <math>X(t)</math> in (\ref{s1_000}) can be expressed as
 \begin{align}\label{s1_001}
    \frac{\partial p(x, t)}{\partial t} &= - \sum^{d}_{i=1}\frac{\partial }{\partial x_{i}} \left[f_{i}(x)  p(x, t)\right] + \sum^{d}_{i,j=1} \frac{\partial ^2}{\partial x_{i}\partial x_{j}}\left[D_{ij}(x)p(x, t) \right],
     \end{align}
-where $D_{ij}(x)= \sum_{k=1}^n \sigma_{ik}(x)\sigma_{kj}(x)$.
+where <math>D_{ij}(x)= \sum_{k=1}^n \sigma_{ik}(x)\sigma_{kj}(x)</math>.
 ==example==

← 이전 판		2020년 11월 13일 (금) 07:24 판
55번째 줄:		55번째 줄:
	[[분류:math and physics]]		[[분류:math and physics]]
	[[분류:probability]]		[[분류:probability]]
		+	[[분류:migrate]]

@@ 6번째 줄: / 6번째 줄: @@
 ==basic probability theory==
-* Let $(\Omega, \mathcal{F}, P)$ be probability space
+* [[Basic probability theory]]
 ==Ito SDE==

← 이전 판		2016년 6월 9일 (목) 02:55 판
67번째 줄:		67번째 줄:

	[[분류:math and physics]]		[[분류:math and physics]]
		+	[[분류:probability]]