The Itô-Tanaka formula usually require that $f$ is the difference of two convex functions. But I do see this condition is used in the proof. I think the proof only needs the fact that $f$ is convex and use the integral representation of a convex function. Why is the reason of this setting?
2026-04-07 06:10:53.1775542253
Assumption in Itô-Tanaka formula
106 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in STOCHASTIC-CALCULUS
- Interpreting stationary distribution $P_{\infty}(X,V)$ of a random process
- Reference request for a lemma on the expected value of Hermitian polynomials of Gaussian random variables.
- Why does there exists a random variable $x^n(t,\omega')$ such that $x_{k_r}^n$ converges to it
- Compute the covariance of $W_t$ and $B_t=\int_0^t\mathrm{sgn}(W)dW$, for a Brownian motion $W$
- Mean and variance of $X:=(k-3)^2$ for $k\in\{1,\ldots,6\}$.
- 4th moment of a Wiener stochastic integral?
- Unsure how to calculate $dY_{t}$
- What techniques for proving that a stopping time is finite almost surely?
- Optional Stopping Theorem for martingales
- $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 STOCHASTIC-INTEGRALS
- Meaning of a double integral
- 4th moment of a Wiener stochastic integral?
- Cross Variation of stochatic integrals
- Stochastic proof variance
- Solving of enhanced Hull-White $dX_t = \frac{e^t-X_t}{t-2}dt + tdW_t$
- Calculating $E[exp(\int_0^T W_s dW_s)]$?
- Applying Ito's formula on a $C^1$ only differentiable function yielding a martingale
- what does it mean by those equations of random process?
- Why aren't the sample paths of this stochastic process defined?
- Is the solution to this (simple) Stochastic Differential Equation unique?
Related Questions in STOCHASTIC-ANALYSIS
- Cross Variation of stochatic integrals
- Solution of an HJB equation in continuous time
- Initial Distribution of Stochastic Differential Equations
- Infinitesimal generator of $3$-dimensional Stochastic differential equation
- On the continuity of Gaussian processes on the interval [0,1] depending on the continuity of the covariance function
- Joint Markov property of a Markov chain and its integral against Brownian Motion
- How can a martingale be a density process?
- Show that for a continuous Gaussian martingale process $M$ that $\langle M, M \rangle_t = f(t)$ is continuous, monotone, and nondecreasing
- Laplace transform of hitting time of Brownian motion with drift
- Is the solution to this (simple) Stochastic Differential Equation unique?
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?
The condition that $f$ is the difference of two convex functions is more general than the condition $f$ is convex. You only need to prove it for the case that $f$ is convex, though, because then the result follows from linearity. So you prove the formula for when $f$ is convex, then immediately conclude the more general case for when $f$ is the difference of two convex functions.