Dan
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Registered User
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May 18 |
answered | Existence of dominating measure for weak*-compact set of measures |
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Apr 12 |
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Absolute continuity of probabilities on Polish spaces and open sets. No: If $P$ is Lebesgue measure on $[0,1]$, then $P(E) > 0$ for every open set $E$, and every probability measure $Q$ on $[0,1]$ vacuously satisfies your assumption. |
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Mar 1 |
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Wasserstein distance between two diffusion processes. Explicit formulas may be too much to hope for in general, but you can certainly bound the distance, at least if the $f_i,\sigma_i$ are Lipschitz. Solve the SDEs strongly, with respect to the same Brownian motion, and then use the inequality $W(P_1,P_2)^2 \le \mathbb{E}[\int_0^T(X_t - Y_t)^2dt]$ along with standard stability estimates. |
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Feb 19 |
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Hausdorff distance and sum of independent variables If $F$ degenerate and $N$ nondegenerate there is no convergence, since $\sigma(F)$ is trivial and $\sigma(F + \epsilon N) = \sigma(N)$ is not. |
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Jan 30 |
answered | Metrization of weak convergence of signed measures |
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Jan 30 |
accepted | Is an L_1 bounded sequence of random variables with uniformly converging CDFs uniformly integrable? |
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Jan 29 |
answered | Is an L_1 bounded sequence of random variables with uniformly converging CDFs uniformly integrable? |
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Dec 29 |
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When is a space of measures a measurable space? @Gerald: Unless I'm missing something, the topology generated by the maps $\mu \mapsto \mu(A)$ for $A \in \Sigma$ is weaker than the total variation topology. In particular, it is not discrete, and its Borel $\sigma$-algebra contains the cylindrical $\sigma$-algebra proposed by Gerald. The inclusion will usually be strict when $\Sigma$ is infinite, as suggested by the nonseparability of the topology. Bogachev's Measure Theory Vol I discusses this topology, beginning on page 291. |
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Dec 22 |
awarded | ● Enthusiast |
