Question

If $X^n$ is a Feller process, $τ_n$ is a stopping time and $h_n\to0$, why can we conclude $|X^n_{τ_n}-X^n_{τ_n+h_n}|→0$ from $|X^n_0-X^n_{h_n}|→0$?

score 106 · Answer 1 · 2026-03-26 19:02:46

106

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If $X^n$ is a Feller process, $τ_n$ is a stopping time and $h_n\to0$, why can we conclude $|X^n_{τ_n}-X^n_{τ_n+h_n}|→0$ from $|X^n_0-X^n_{h_n}|→0$?

Published on 26 Mar 2026 - 19:02

score 25 · Answer 2 · 2019-03-18 08:53:57

25

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score 72 · Answer 3 · 2019-03-18 12:36:08

72

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167

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176

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401

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342

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62

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score 550 · Answer 15 · 2019-04-05 03:17:22

550

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List Question

If $X^n$ is a Feller process, $τ_n$ is a stopping time and $h_n\to0$, why can we conclude $|X^n_{τ_n}-X^n_{τ_n+h_n}|→0$ from $|X^n_0-X^n_{h_n}|→0$?

How should I adapt my continuous model to the discrete data records?

Prove that $\lim_{L\rightarrow\infty} P\left(\sup_{0\leq s\leq t}|B(s)|>L\right)=0$, for each $t\geq0$, where $B$ standard Brownian motion.

Uniform integrablility of Radon-Nikodym derivatives if measures are locally equivalent.

Questions about Quadratic Variation given by Brownian Motion

Proving Ito Isometry using Functional Analysis

Unit used in continuous time process noise matrix in kalman filters, when STD is from discrete time data

Mean perimeter for random triangle inscribed in the unit circle

Expectations of Ito integral

Proving Girsanov Theorem

How to bound increments of Ito integral?

Distribution and convergence in law of the discontinuous random functions

Looking for a book about mathematical proof of technical analysis in trading stocks!

Differential of traders wealth function equals $0$. Correct?

Justification of interchanging Expectation and Limit in Ito Integral Approximation

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