Calculating Conditional Probability for Poisson Processes

Thread starter gradnu
Start date Jan 14, 2008
Tags

Conditional

Jan 14, 2008

gradnu

Let {Nt, t>0} be a Poisson process with arrival rate \lambda.
Consider a process {Xt = exp(Nt-a*t, t>0}.
How to calculate E[Xt|Xs] for 0<s<t.

Physics news on Phys.org

Vortices in ultralight dark matter halos could reveal new clues to cosmic structure
Taking the shock out of predicting shock wave behavior with precise computational modeling
Algorithm precisely quantifies flow of information in complex networks

Jan 21, 2008

EnumaElish

Science Advisor

By simulation?

Jan 25, 2008

gradnu

No. Analytically on paper.

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...

View full post »