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Results tagged with stochastic-calculus
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user 11768
Stochastic calculus provides a consistent theory of integration for stochastic processes and is used to model random systems. Its applications range from statistical physics to quantitative finance.
6
votes
1
answer
4k
views
Time-dependent Markov process: infinitesimal generator
If one talks about homogeneous Markov diffusion
$$
\mathrm dX_t = \mu(X_t)\mathrm dt+\sigma(X_t)\mathrm dw_t
$$
with $\mu,\sigma$ sufficiently differentiable and of appropriate dimensions, there is ni …
- 1,655
3
votes
1
answer
672
views
Reachability for Markov process, continuous time
Let $X$ be a strong Markov process in the continuous time with a state space $\mathbb R^n$. Consider a reachability problem for this process, i.e.
$$
v(x):=\mathsf P_x(X_t\in A\text{ for some }0\leq t …
- 1,655
2
votes
2
answers
2k
views
Change of measure Markov process
We begin with example. For the Poisson process with an intensity $\lambda_1$ there is an equivalent change of measure which makes it intensity to $\lambda_2$.
I would like to find the conditions whe …
- 1,655
2
votes
Accepted
Upper bound concerning Snell envelope
I think it is just a sequence of much stronger inequalities that goes as follows. All the inequalities below are $\Bbb P$-a.s.
Let $\tau\in \mathcal T_{t,T}$ be an arbitrary stopping time, then
$$
…
- 1,655