All Questions

Consider the well-known comparison theorem for SDEs, versions of which appear in several textbooks, e.g., Karatzas and Shreve, Proposition 5.2.18, or Revuz and Yor, Theorem IX.3.7. The result states ...

One way to state (omitting technical requirements) the Feynman-Kac formula that I am familiar with is as follows. Let $u$ be a solution to the pde $$u_t(x,t)=-\frac{\sigma^2(x,t)}2u_{xx}(x,t)-V(x,t)u(...

Is there a way to simulate an $N$-dimensional geometric Brownian motion i.e. variable $$x_i, i \in [1, N] $$ is diffusing in log-space such that $$\log (x_i)$$ follows a Brownian motion with a given ...

Let $b:\mathbb R^d \to \mathbb R^d$ and $\sigma:\mathbb R^d \to \mathcal M_{ d\times q} (\mathbb R)$ be Lipschitz. Let $(W_t, t\ge 0)$ be the standard $q$-dimensional Brownian motion. Then $$ d X_t = ...

In various places, an example being https://projecteuclid.org/download/pdf_1/euclid.aoap/1034625254, the authors consider a discrete-time process (real-valued, say) $(X_n)_{n \in \mathbb{N}}$, define ...

Florin Soucaliuc published the following research announcement in 2002 containing some results from his thesis on reflected diffusion processes: [1] F. Soucaliuc, Réflexion entre deux diffusions ...