User UBM

5 votes

3 answers

466 views

Approximating a general process by a simple process in definition of integration wrt Brownian motion

asked Aug 21, 2019 at 11:10

5 votes

1 answer

299 views

A case where a stochastic exponential is a true martingale

asked Jan 29, 2020 at 17:31

4 votes

1 answer

36 views

Show that $P(B)>0$ where $B = \{\tau < T \text{ and } |X_t| \leq \theta -1 \text{ for all } 0 \leq t \leq \tau\}$ and $X$ is the sol of an Ito SDE

asked Dec 16, 2020 at 15:50

3 votes

3 answers

709 views

if $M$ is a UI - martingale then $M_t \rightarrow M_{\infty}$ in $L^1$

asked Jan 1, 2020 at 23:50

2 votes

1 answer

281 views

Exponential submartingale inequality

asked May 15, 2022 at 15:44

2 votes

0 answers

66 views

If we have $(\Omega, \mathscr{F}, P)$ and a filtration $\{\mathscr{F}_t^W; 0 \leq t \leq T\},$ how can we justify that $\mathscr{F} = \mathscr{F}_T$?

asked Dec 19, 2019 at 20:34

2 votes

1 answer

161 views

Is it possible to obtain the Radon-Nikodym derivative $\left. \frac{dQ}{dP} \right|_{\mathscr{F}}$ from a UI martigale?

asked Dec 22, 2019 at 11:13

2 votes

1 answer

384 views

Example of stochastic process that is adapted but not predictable

asked Nov 22, 2019 at 15:24

1 vote

0 answers

29 views

Let $P \sim Q$. Is it true that if (the r.v.) $X \in L^2(\Omega, \mathscr{F},P)$ then $X \in L^2(\Omega, \mathscr{F},Q)$?

asked Nov 27, 2019 at 14:42

1 vote

1 answer

124 views

Given a prob measure P and a P-UI martingale $\{ \rho_t \}$ define $Q \sim P$ s.t. $E[\frac{dQ}{dP}|\mathscr{F}_t]=\rho_t$

asked Dec 13, 2019 at 0:31

1 vote

1 answer

348 views

Holder inequality with $q = \infty$

asked Jan 1, 2020 at 17:44

1 vote

0 answers

106 views

How can I prove that the solution to this SDE is a Markov process?

asked Jan 31, 2020 at 15:01

1 vote

0 answers

46 views

Let $\{ X^{\tau_n} \}$ be a sequence continuous stopped process. Does $E[X_t^{\tau_n}]<C$ for all $n \in \mathbb N$ imply that $E[X_t]<C$?

asked Feb 7, 2020 at 19:35

0 votes

2 answers

342 views

X is a predictable proccess iff X is $\{ F_{t^-}\}$-adapted?

asked Nov 22, 2019 at 18:10

Stack Exchange Network

14 Questions

Approximating a general process by a simple process in definition of integration wrt Brownian motion

A case where a stochastic exponential is a true martingale

Show that $P(B)>0$ where $B = \{\tau < T \text{ and } |X_t| \leq \theta -1 \text{ for all } 0 \leq t \leq \tau\}$ and $X$ is the sol of an Ito SDE

if $M$ is a UI - martingale then $M_t \rightarrow M_{\infty}$ in $L^1$

Exponential submartingale inequality

If we have $(\Omega, \mathscr{F}, P)$ and a filtration $\{\mathscr{F}_t^W; 0 \leq t \leq T\},$ how can we justify that $\mathscr{F} = \mathscr{F}_T$?

Is it possible to obtain the Radon-Nikodym derivative $\left. \frac{dQ}{dP} \right|_{\mathscr{F}}$ from a UI martigale?

Example of stochastic process that is adapted but not predictable

Let $P \sim Q$. Is it true that if (the r.v.) $X \in L^2(\Omega, \mathscr{F},P)$ then $X \in L^2(\Omega, \mathscr{F},Q)$?

Given a prob measure P and a P-UI martingale $\{ \rho_t \}$ define $Q \sim P$ s.t. $E[\frac{dQ}{dP}|\mathscr{F}_t]=\rho_t$

Holder inequality with $q = \infty$

How can I prove that the solution to this SDE is a Markov process?

Let $\{ X^{\tau_n} \}$ be a sequence continuous stopped process. Does $E[X_t^{\tau_n}]<C$ for all $n \in \mathbb N$ imply that $E[X_t]<C$?

X is a predictable proccess iff X is $\{ F_{t^-}\}$-adapted?