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# All Questions

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### Ito's Formula for functions that are $C^2$ a.e

In the conventional Ito's formula, it is required that $F$ is $C^2$ everywhere. However I've seen mentioning of a slightly weaker condition, where $F$ is $C^1$ everywhere but $C^2$ a.e.. Is there any ...
43 views

59 views

### Mean field games approximate Nash equilibria

I am learning mean field games (MFG) through the notes by Cardaliaguet: https://www.ceremade.dauphine.fr/~cardaliaguet/MFG20130420.pdf. I have a question about a step in theorem 3.8 on page 17. Let ...
89 views

### Triangle inequality for Ito integral?

For Lebesgue integrals one has the triangle inequality saying that for continuous functions let's say $$\left\vert\int_0^t f(s) \ ds\right\vert \le \Vert f \Vert_{\infty} \int_0^t \ ds$$ Now if ...
99 views

### Random process - autocorrelation

I am currently working on random processes. Let's consider the random process defined as $u^s(x,t) = 2\sum_{n=1}^{N} \hat{u}^n \cos(\kappa^n\cdot x + \psi_n + \omega_n t )\sigma^n$ where $\hat{u}^n$,...
73 views

### “Сross сubic variation” of two Brownian motions and interpretation of the simulation result

Consider two independent 1-dimensional Brownian motions $W_{t},B_{t}$, with an equidistant partition of the interval $[0,T]$, and $n\Delta≡T$. How to calculate the expression below? Can we rewrite ...
73 views

### The probability distribution of “derivative” of a random variable

Disclaimer: Cross-posted in math.SE. Let me set the stage; Consider a stochastic PDE, which has to following form $$\partial_t h(x,t) = H(x,t) + \chi(x,t),$$ where $H$ is a deterministic function, ...
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### Uniqueness of martingale problem for Levy type operator

Consider the following Levy type operator: $$L_t\varphi(x)=\int_{R^d}\big[\varphi(x+z)-\varphi(x)-1_{|z|\leq 1}z\cdot\nabla\varphi(x)\big]\kappa(x,z)\nu(dz),\quad\forall \varphi\in C_c^2(R^d),$$ ...
206 views

I'm trying to understand a calculation in this paper (equation (3.8)). With some details removed, the setup is as follows. Let $G$ be a Lie group, and $g(t)$ a curve in $G$ satisfying the SDE $$dg(t)... 1answer 149 views ### Stochastic Calculus vs Stochastic Processes in Finance [closed] I'm a second year student, interested in financial mathematics, who's trying to plan out his degree path currently. There's a stochastic processes unit offered in year 3 and a stochastic calculus unit ... 0answers 51 views ### Distances between up and down crosses in Gaussian Processes Given a gaussian process g := \mathcal{GP}\left(\mu, \Sigma \right), where \mu is the mean and \Sigma is the covariance function, I am interested in estimating the mean value L_m of the ... 0answers 73 views ### Sufficient conditions for taking limits in stochastic partial differential problems Let's say we have a Cauchy problem:$$ (1) \hspace{0.5cm} u_t (x,t)+A(u) \cdot u_x (x,t)=\nu \cdot u_{xx} (x,t) + \epsilon \cdot f(u) \cdot W, (2) \hspace{0.5cm} u(x,0)=u_0(x),  where $x \in ... 0answers 42 views ### Maximal inequalities of stochastic integral with respect to Poisson random measures Let$\Phi$be a smooth convex function such that$\Psi(x)/|x|\to\infty$as$|x|\to\infty$, and$\hat N(d z,ds)$be a compensated Poisson measure on$R^d\times R_+\$. Do we have the following inequality:...

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