# Questions tagged [stochastic-analysis]

Questions about stochastic analysis or stochastic calculus, for example the Ito integral. See https://en.wikipedia.org/wiki/Stochastic_calculus

1,193 questions
7 views

42 views

### Prove that $\lim_{L\rightarrow\infty} P\left(\sup_{0\leq s\leq t}|B(s)|>L\right)=0$, for each $t\geq0$, where $B$ standard Brownian motion.

Let $B(t)$, $t\geq0$, be a standard Brownian motion. I would like to prove that $$\lim_{L\rightarrow\infty} P\left(\sup_{0\leq s\leq t}|B(s)|>L\right)=0,$$ for each $t\geq0$. In my class notes, ...
20 views

### How should I adapt my continuous model to the discrete data records?

Let $N(t) :N \in \mathbb{N}, t \in \mathbb{R}$ a stochastic jumping process over the time. $N(t)$ is characterized by a unknown pmf (probability mass function) and represents the number of jumps ...
25 views

42 views

6 views

### Ucp convergence and Emery Topology

maybe you can help me once again. It is known that convergence in the semimartingale topology (Emery topology) implies ucp convergence. Can you think of an easy example, to show that the converse is ...
32 views

### Solving a stochastic differential equationn

Does anyone has ideas on how to solve this equation. $$dX_{t} = \left(\sqrt{1+X_{t}^{2}} + \frac{1}{2}X_{t}\right)\,dt + \sqrt{1 + X_{t}^{2}} \,dBt$$ where $Bt$ is a standard Brownian Motion. I have ...
15 views

67 views

### Why do we need absolute continuity of $\langle M \rangle_t(\omega)$ with repect to the Lebesgue measure?

I am trying to understand the proof of proposition 3.2.6 in Stochastic Calculus and Brownian Motion by Karatzas and Shreve. For $X$ bounded they use Lemma 3.2.4 in the same book and eventually claim(...
87 views

### Extending the domain of the Dirichlet form associated with a symmetric Markov semigroup

Let $(E,\mathcal E)$ be a measurable space $\mathcal M_b(E,\mathcal E):=\left\{f:E\to\mathbb R\mid f\text{ is bounded and }\mathcal E\text{-measurable}\right\}$ $(P_t)_{t\ge0}$ be a Markov semigroup ...
31 views

### Probability question with intuitive answer - odds two travelers overlap at the same time?

Let's say Person A sets out from Point X at 8:00 AM on Day 1 and travels for 12 hours until he reaches Point Y at 8:00 PM. Person B sets out from Point Y at 8:00 AM on Day 2 and travels for 12 hours ...
109 views

### Show that the carré du champ operator is nonnegative

Let $(E,\mathcal E)$ be a measurable space $\mathcal M_b(E,\mathcal E):=\left\{f:E\to\mathbb R\mid f\text{ is bounded and }\mathcal E\text{-measurable}\right\}$ $(\kappa_t)_{t\ge0}$ be a Markov ...
65 views

60 views

Let $(\Omega,\mathcal A,\operatorname P)$ be a probability space $b,\sigma:\mathbb R\to\mathbb R$ be Lipschitz continuous $(X_t^x)_{t\ge0}$ be a continuous process on $(\Omega,\mathcal A,\... 1answer 35 views ### Estimate for the distance from the initial value of a strong solution of an SDE Let$(\Omega,\mathcal A,\operatorname P)$be a probability space$b,\sigma:\mathbb R\to\mathbb R$be Lipschitz continuous$(X_t^x)_{t\ge0}$be a continuous process on$(\Omega,\mathcal A,\...
Let consider an urn model containing $n$ balls such that $m_g$ balls are green, $m_r$ are red and $m_b$ are blue and we have $n = m_g + m_r +m_b$. Especially this means that the $m_g$ green balls are ...