List questions from martingales

Published on 12 Apr 2026 - 13:44

69

Views

For any Markov chain $X_n$, if the generator has $\mathscr{L}f \le -c$ for nonnegative $c$ then $f(X_n)+\sum_{i<n}c(X_i)$ is a martingale

Published on 27 Jan 2022 - 18:04

23

Views

Why is $X(T)$ under $\mathbb Q^{M}$ $\sim X(T)-X(0)+\tilde{X}(0)$ under $\mathbb Q^ {N}$ under the following assumptions?

Published on 29 Jan 2022 - 13:18

147

Views

Showing $M_n = M_{n-1}^2 U_n^{M_{n-1}-1}$ is a martingale.

Published on 31 Jan 2022 - 11:50

210

Views

Prove that $X_t = W_t \mathbb{1}(\tau > t) + (2W_{\tau} - W_t) \mathbb{1}(\tau \le t)$ is a martingale.

Published on 31 Jan 2022 - 12:41

52

Views

How to show that $E(1_{T_y<\infty}M_{T_y})=yE(1_{T_y<\infty})$?

Published on 13 Apr 2026 - 12:49

72

Views

The average time before the first appearance of a sequence of a length 3 of Bernoulli r.v.

Published on 12 Apr 2026 - 22:17

123

Views

A discrete local martingale which is integrable for some random $T>0$ is a true martingale up to time $T$.

Published on 13 Apr 2026 - 3:54

59

Views

Martingale Convergence under equivalent probability measures

Published on 13 Apr 2026 - 16:21

146

Views

Monotonical Lévy's Upward Theorem

Published on 11 Apr 2026 - 14:05

162

Views

Martingale is Uniformly Integrable

Published on 13 Apr 2026 - 7:33

197

Views

If $X_n$ and $Y_n$ are submartingales w.r.t. $\mathcal{F}_n$, then $X_n \lor Y_n$ is also.

Published on 08 Feb 2022 - 3:35

90

Views

A martingale and mesurability problem

Published on 13 Apr 2026 - 6:08

73

Views

Preservation of the local martingale property under the right-continuous filtration

Published on 11 Apr 2026 - 22:30

41

Views

Citation for a theorem about filtrations

Published on 12 Apr 2026 - 21:31

List Question

Martingales and Markov chain

For any Markov chain $X_n$, if the generator has $\mathscr{L}f \le -c$ for nonnegative $c$ then $f(X_n)+\sum_{i<n}c(X_i)$ is a martingale

Why is $X(T)$ under $\mathbb Q^{M}$ $\sim X(T)-X(0)+\tilde{X}(0)$ under $\mathbb Q^ {N}$ under the following assumptions?

Showing $M_n = M_{n-1}^2 U_n^{M_{n-1}-1}$ is a martingale.

Prove that $X_t = W_t \mathbb{1}(\tau > t) + (2W_{\tau} - W_t) \mathbb{1}(\tau \le t)$ is a martingale.

How to show that $E(1_{T_y<\infty}M_{T_y})=yE(1_{T_y<\infty})$?

The average time before the first appearance of a sequence of a length 3 of Bernoulli r.v.

A discrete local martingale which is integrable for some random $T>0$ is a true martingale up to time $T$.

Martingale Convergence under equivalent probability measures

Monotonical Lévy's Upward Theorem

Martingale is Uniformly Integrable

If $X_n$ and $Y_n$ are submartingales w.r.t. $\mathcal{F}_n$, then $X_n \lor Y_n$ is also.

A martingale and mesurability problem

Preservation of the local martingale property under the right-continuous filtration

Citation for a theorem about filtrations

Trending Questions

Popular # Hahtags

Popular Questions