I pray to kindly show the intuition behind the concept of rough path. Google provided some links that deal with the notion of rough path but was difficult for me to have an idea.
2026-03-28 23:11:51.1774739511
Intuition for Rough path
518 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in INTUITION
- How to see line bundle on $\mathbb P^1$ intuitively?
- Intuition for $\int_Cz^ndz$ for $n=-1, n\neq -1$
- Intuition on Axiom of Completeness (Lower Bounds)
- What is the point of the maximum likelihood estimator?
- Why are functions of compact support so important?
- What is it, intuitively, that makes a structure "topological"?
- geometric view of similar vs congruent matrices
- Weighted average intuition
- a long but quite interesting adding and deleting balls problem
- What does it mean, intuitively, to have a differential form on a Manifold (example inside)
Related Questions in BROWNIAN-MOTION
- Compute the covariance of $W_t$ and $B_t=\int_0^t\mathrm{sgn}(W)dW$, for a Brownian motion $W$
- Why has $\sup_{s \in (0,t)} B_s$ the same distribution as $\sup_{s \in (0,t)} B_s-B_t$ for a Brownian motion $(B_t)_{t \geq 0}$?
- Identity related to Brownian motion
- 4th moment of a Wiener stochastic integral?
- Optional Stopping Theorem for martingales
- Discontinuous Brownian Motion
- Sample path of Brownian motion Hölder continuous?
- Polar Brownian motion not recovering polar Laplacian?
- Uniqueness of the parameters of an Ito process, given initial and terminal conditions
- $dX_t=\alpha X_t \,dt + \sqrt{X_t} \,dW_t, $ with $X_0=x_0,\,\alpha,\sigma>0.$ Compute $E[X_t] $ and $E[Y]$ for $Y=\lim_{t\to\infty}e^{-\alpha t}X_t$
Related Questions in BOUNDED-VARIATION
- Method for evaluating Darboux integrals by a sequence of partitions?
- Function of bounded variation which is differentiable except on countable set
- Variation with respect to the projective tensor norm of a matrix of bounded variation functions
- Associativity of an integral against a function with finite variation
- Suppose $f(x)$ is of bounded variation. Show $F(x) = \frac{1}{x} \int_0^x f(t) \, dt$ is also of bounded variation.
- Is there a sufficient condition for which derivative of $\sum_{n=0}^{\infty} a_n x^n$ is bounded for all $x \in \mathbb{R}$?
- Looking for the name of this property, if it has one.
- Bounded Variation Proof
- Rearranging a sequence of bounded variation
- If $f$ is $g$-Riemann-Stieltjes integrable on $[a,b]$, prove that it's $g$-RS-integrable on $[a,c] \subset [a,b]$
Related Questions in HOLDER-SPACES
- Embeddings between Hölder spaces $ C^{0,\beta} \hookrightarrow C^{0, \alpha} .$
- Holder seminorm of log inequality
- Is it a equivalent semi norm in Campanato space?
- Finite dimensionality of the "deRham cohomology" defined using $C^{k,\alpha}$ forms instead of smooth forms.
- Question on definition of $\;\alpha-$Holder norms
- Piecewise Holder functions
- What is little Holder space?
- What about an approximation of the Hölder's constant associated to $\sum_{n=0}^\infty\gamma^n\cos(11^n\pi x)$, where $\gamma$ is the Euler's constant?
- Is the power of a Holder continuous function still Holder continuous?
- Does taking a fractional derivative remove a fractional amount of Holder regularity?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
A rough path is an interesting analytical and algebraic object:
algebraic: it's a multiplicative functional in a (truncated) tensor algebra obeying Chen's Theorem (non-commutative analogue of the additivity of integration - Chasle's relation).
analytic: it's of finite p-variation
the best place to start is to read T. Lyons et al's St. Flour notes "Differential equations driven by rough paths".