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1d
reviewed Approve Real roots of the equation $\frac{18}{x^4} + \frac{1}{x^2} = 4$
1d
revised Lévy Process existence of the expectation of the supremum of the past process.
correcting for accents
1d
comment Compute $\frac{d}{dt}\int_0^t e^{x(s)}ds$, where $x$ is a standard Brownian motion.
@ Dave ddd : Well no it's not and Marc is right. Best regards.
2d
reviewed Approve Is there any better way to find n! without just multiplying all the numbers till n?
2d
reviewed Approve Different Ids on mars
Feb
9
comment If $dX_{t} = X_{t}\,dt + \,dB_{t}$, why does $e^{- t}dX_{t} = e^{-t} X_{t} \,dt + e^{-t} \,dB_{t}$?
@user46944 : use the hint of Kolmo with Itô's lemma. Best regards
Feb
9
revised How to show that this is a martingale?
edited body
Feb
9
comment How to show that this is a martingale?
@Ant : Welcome. As a last remark, you see that you get the "square integrable property" for the same price. Best regards.
Feb
9
answered How to show that this is a martingale?
Feb
9
comment How to show that this is a martingale?
Check Lemma 3 on George Lowther's website - here almostsure.wordpress.com/2010/03/25/… . NB: I suppose that $W$ is a Brownian motion which is a square integrable martingale. Best regards
Feb
9
reviewed Approve How to I find the distribution of $\log p(X)$ when $X$ is distributed under $p$?
Feb
9
comment What is the difference between a martingale and doob's martingale?
@ Tony Clayton : Would please give us of your definition of a Doob martingale. Best regards
Feb
8
comment Joint convergence of stochastic processes
some clarification are needed about your notations $X_n(t)\overset{d}{\longrightarrow} X(t)$ are you claiming that this is true for every $t$ or that convergence of X_n to X holds on the probability space supporting the trajectories of X and X_n ? Best regards.
Feb
8
comment Ito Formula for Stochastic Integral
@Kenneth Chen : well as long as your process S is well defined (i.e. the sde has a solution) your process $y_t$ is correctly defined and the differential form is simply : $dy_t=S_tdt+S_tdW_t$ no more, no less. Your formulas are certainly all wrong. Best regards
Feb
8
comment Stochastic process independent of its future
Every Markov Process that is predictable fulfill this condition and this is quite general, for example any diffusion process enjoy this property. Best regards.
Feb
8
comment $L^p$ integrable local martingale is still $L^p$ integrable when stopped at localizing stopping times.
@ webbster : Well unless mistaken a positive local martingale is a super-martingale not a sub-martingale (look at lemma 2 : almostsure.wordpress.com/2009/12/24/local-martingales/…;. In the end I agree with you that my argument seems fishy. Best regards.
Feb
5
reviewed Approve Random selection in percentage
Feb
5
comment A clarification on $L_{loc}^2$ process and stochastic exponential
Otherwise said 10.3 implies 4.34 but not the other way around. Or again almost sure finiteness does not implies almost sure boundedness but the opposite is true. Best regards
Feb
5
comment A functional of a Lévy process
@ Billy Pilgrim : What kind of results are you looking for ? The question is I am afraid a bit too general, and the only thing that comes to my mind is hum Itô's lemma ... best regards.
Feb
5
revised A functional of a Lévy process
added 5 characters in body; edited title