# Questions tagged [stochastic-differential-equations]

Stochastic differential equations (SDE) occur where a system described by differential equations is influenced by random noise. Stochastic differential equations are used in finance (interest rate, stock prices, …), biology (population, epidemics, …), physics (particles in fluids, thermal noise, …), and control and signal processing (controller, filtering, …).

1,186 questions
Filter by
Sorted by
Tagged with
40 views

28 views

• 3
30 views

• 1
62 views

### Is a Riccati BSDE explicitly solvable?

Let $W=\{W_t\}_{t\in[0;T]}$ be a real-valued Brownian motion, $\{F_t\}_{t\in [0;T]}$ the filtration generated by $W$, augmented with the nullsets, let $C\in (0;\infty)$ and $\{a_t\}_{t\in[0;T]}$ be a ...
• 495
15 views

### $dS_t=\mu S_t dt +\sigma S_t^{\alpha/2} d W_t$ and $Y_t=S^{2-\alpha}$, can one simulate exact paths for Y_t?

The task states that $dS_t=\mu S_t dt +\sigma S_t^{\alpha/2} d W_t$ and the question is if one can generate (simulate) exact paths for $S_t$ by taking the transformation s.t. $Y_t=S_t^{2-\alpha}$. I ...
• 21
47 views

### Solving a linear backward stochastic differential equation

Let $W=\{W_t\}_{t\in[0;T]}$ be a real-valued Brownian motion, $\{F_t\}_{t\in [0;T]}$ the filtration generated by $W$, augmented with the nullsets, let $\{B_t\}_{t\in[0;T]}$ be an adapted process and ...
• 495
39 views

### Correlation function in the Langevin equation

So the Langevin equation of Brownian motion is a stochastic differential equation defined as $$m {d \textbf{v} \over{dt} } = - \lambda \textbf{v} + \eta(t)$$ where the noise function $\eta(t)$ has ...
26 views

• 1,904
78 views

### Verify process is an Ito process

Let $(\xi(t),t\ge 0)$ be an Ito process with $\xi(0)=\theta$ and $$d\xi(t)=\kappa(\theta-\xi(t))dt+\sigma\sqrt{\xi(t)}dW(t)$$ for $\kappa, \theta, \sigma \in \mathbb{R}$. Show that $(\eta(t),t\ge 0)$,...
16 views

### Deriving Stochastic Differential Equations about Population Dynamics

This is somewhat of a high-level, I-hardly-know-much-about-the-topic-yet question, but here goes. I came across online a presentation in which part of it documented deriving an SDE for a population ...
46 views

• 828
36 views

### Infinite variation of Brownian motion and Continuity

Let $C>0$ be a constant. Brownian motion is Hölder continuous for $\alpha=1/2$: $$| B(t+h) - B(t) | \leq C \sqrt{h \log(1/h)} \leq C h^\alpha,$$ for every sufficiently small $h$. But Brownian ...
• 41