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vaoy
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accepted
If $f\in C([0,\infty))$, does $\delta>0$ and $g\in C^1((0,\delta))\cap C([0,\delta])$ s.t. $g\geq f$ on $[0,\delta]$ and $g(0)=f(0)$ exist?
asked
If $f\in C([0,\infty))$, does $\delta>0$ and $g\in C^1((0,\delta))\cap C([0,\delta])$ s.t. $g\geq f$ on $[0,\delta]$ and $g(0)=f(0)$ exist?
revised
$f \in L^2(X\times Y,\mu \times K)$ for Kernel $K$, is the map $X \ni x \mapsto (f(x,\cdot),x) \in \bigsqcup_{x \in X}L^2(Y,\Sigma_Y,K_x)$ measurable?
added 1 character in body
asked
$f \in L^2(X\times Y,\mu \times K)$ for Kernel $K$, is the map $X \ni x \mapsto (f(x,\cdot),x) \in \bigsqcup_{x \in X}L^2(Y,\Sigma_Y,K_x)$ measurable?
awarded
 Popular Question
comment
Increasing stochastic process
How do you justify that this $\widetilde X$ is actually a modification of the original process $X$?
awarded
 Yearling
comment
If $(\alpha_t)$ is $\mathbb{F}^X$-progressive for a continuous process $(X_t)$, can we write $\alpha_t = \tilde{\alpha}(t,X)$?
@rubikscube09 yes, exactly.
revised
If $(\alpha_t)$ is $\mathbb{F}^X$-progressive for a continuous process $(X_t)$, can we write $\alpha_t = \tilde{\alpha}(t,X)$?
deleted 2 characters in body
asked
If $(\alpha_t)$ is $\mathbb{F}^X$-progressive for a continuous process $(X_t)$, can we write $\alpha_t = \tilde{\alpha}(t,X)$?
awarded
 Curious
comment
Is the topology generated by the convergence of finite-dimensional distributions metrizable?
Do you mean for $\mathbf{D}$? If so, then yes as $\mathbf{D}$ is polish.
asked
Is the topology generated by the convergence of finite-dimensional distributions metrizable?
accepted
How to interpret couplings in optimal transport?
asked
How to interpret couplings in optimal transport?
comment
Why are financial markets modeled by càdlàg processes?
Some process that has a double jump. For example, $X_t := 1_{[0,t_0)} + 2 \cdot 1_{(t_0,T]}$ for $0 < t_0 < T < \infty$.
awarded
 Custodian
reviewed
Approve
Why are financial markets modeled by càdlàg processes?
asked
Why are financial markets modeled by càdlàg processes?
accepted
When does the predictable $\sigma$-algebra $\mathcal{P}$ coincide with the optional $\sigma$-algebra $\mathcal{O}$?
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