Stochastic differential equations in which the drift is a quadratic function of the state variable and the infinitesimal standard deviation is proportional to the state variable are pervasive in electrical engineering, signal processing, the neurosciences, and the management sciences. Within this class, the homogeneous case in which the drift term contains no constant parameter is well-understood but the inhomogeneous case remains less researched. The basic issues of existence, positivity and explosion of solutions for the inhomogeneous case are addressed in this paper. It is shown that these results help settle an ambiguous issue arising in a fundamental neuroscience model and are of potential value in a class of signal processing models arising in electrical engineering.
|Original language||English (US)|
|Title of host publication||Cerebrospinal Fluid|
|Subtitle of host publication||Functions, Composition and Disorders|
|Publisher||Nova Science Publishers, Inc.|
|Number of pages||15|
|State||Published - Aug 1 2012|
- Gronwall inequality
- Quadratic drift.
- Signal processing models
- Stochastic differential equations
- Strong solutions
- The it̂o formula
ASJC Scopus subject areas