Standard Chemical Master Equation (Q6773624): Difference between revisions

@@ Property / community @@
+MathModDB
@@ Property / community: MathModDB / rank @@
+Normal rank
@@ Property / instance of @@
+mathematical expression
@@ Property / instance of: mathematical expression / rank @@
+Normal rank
@@ Property / MaRDI profile type @@
+MaRDI formula profile
@@ Property / MaRDI profile type: MaRDI formula profile / rank @@
+Normal rank
@@ Property / defining formula @@
+ $\frac{d}{d t} p (𝒙, t) = \sum_{j = 1}^{11} [f_{j} (𝒙 - 𝒗_{j}) p (𝒙 - 𝒗_{j}, t) - f_{j} (𝒙) p (𝒙, t)]$ 
\frac{d}{d t} p(\boldsymbol{x}, t)=\sum_{j=1}^{11}\left[f_j\left(\boldsymbol{x}-\boldsymbol{v}_j\right) p\left(\boldsymbol{x}-\boldsymbol{v}_j, t\right)-f_j(\boldsymbol{x}) p(\boldsymbol{x}, t)\right]
+Normal rank
@@ Property / in defining formula @@
+ $p (x, t)$ 
p(x, t)
@@ Property / in defining formula: $p (x, t)$ / rank @@
+Normal rank
@@ Property / in defining formula: $p (x, t)$ / qualifier @@
+symbol represents: Probability of the System being in a State
@@ Property / in defining formula @@
+ $X (t)$ 
X(t)
@@ Property / in defining formula: $X (t)$ / rank @@
+Normal rank
@@ Property / in defining formula: $X (t)$ / qualifier @@
+symbol represents: Markov Jump Process
@@ Property / in defining formula @@
+ $v_{j}$ 
v_j
@@ Property / in defining formula: $v_{j}$ / rank @@
+Normal rank
@@ Property / in defining formula: $v_{j}$ / qualifier @@
+symbol represents: Stoichiometric Vectors
@@ Property / in defining formula @@
+ $f_{j}$ 
f_j
@@ Property / in defining formula: $f_{j}$ / rank @@
+Normal rank
@@ Property / in defining formula: $f_{j}$ / qualifier @@
+symbol represents: Propensity functions for the signalling of G‑protein coupled receptors reactions
@@ Property / in defining formula @@
+ $x$ 
x
@@ Property / in defining formula: $x$ / rank @@
+Normal rank
@@ Property / in defining formula: $x$ / qualifier @@
+symbol represents: State of System Vector
@@ links / mardi / name / links / mardi / name @@
+Formula:6773624

Standard Chemical Master Equation (Q6773624): Difference between revisions

ddtp(𝒙,t)=∑j=111[fj(𝒙−𝒗j)p(𝒙−𝒗j,t)−fj(𝒙)p(𝒙,t)]

p(x,t)

X(t)

vj

fj

x

Latest revision as of 08:18, 11 July 2025

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Mathematics(1 entry)

$\frac{d}{d t} p (𝒙, t) = \sum_{j = 1}^{11} [f_{j} (𝒙 - 𝒗_{j}) p (𝒙 - 𝒗_{j}, t) - f_{j} (𝒙) p (𝒙, t)]$

$p (x, t)$

$X (t)$

$v_{j}$

$f_{j}$

$x$