The Novikov and entropy conditions of multidimensional diffusion processes with singular drift

On Stochastic Differential Equations with Locally Unbounded Drift

“…Such equations arise in stochastic mechanics, and have extensively been studied in literature (see e.g. [1], [14], [15], [16], [17], [21] and the references therein). Portenko [18] proves the existence and the uniqueness in law of the weak…”

Consistent fitting of one-factor models to interest rate data

“…in the books of Liptser and Shiryayev (1977), Rogers and Williams (1987), Karatzas and Shreve (1991) and, e.g. in the papers of Stummer (1990Stummer ( , 1993Stummer ( , 2000) one gets the dynamics of the short rate process r t under the risk neutral measure Q: Revuz and Yor (1991), there is a simple expression for the density martingale. However, for starting short rate levelr 0 = 0, the laws for different dimension are mutually singular; the escape rates from the short rate level 0 are different.…”

On weak solutions of SDEs with singular time-dependent drift and driven by stable processes

“…However, it turns out that the Lipschitz-continuity on the drift is far from being necessary; this is well demonstrated in the special case where α = 2, that is, when S is a d-dimensional Brownian motion. Indeed, there is an extensive literature devoted to the study of Brownian motion (or more generally, diffusions) with singular drift, see, e.g., [26,22,16,21,1,13,6,24], and many others. In particular, it was shown in [13] that if S is a Brownian motion and there exist p, q > 0 with d/p + 2/q < 1 such that b ∈ L q loc (R + ; L p (R d )), namely…”