2,861 research outputs found
Long-time behaviour of degenerate diffusions: UFG-type SDEs and time-inhomogeneous hypoelliptic processes
We study the long time behaviour of a large class of diffusion processes on
, generated by second order differential operators of (possibly)
degenerate type. The operators that we consider {\em need not} satisfy the
H\"ormander condition. Instead, they satisfy the so-called UFG condition,
introduced by Herman, Lobry and Sussman in the context of geometric control
theory and later by Kusuoka and Stroock, this time with probabilistic
motivations. In this paper we study UFG diffusions and demonstrate the
importance of such a class of processes in several respects: roughly speaking
i) we show that UFG processes constitute a family of SDEs which exhibit
multiple invariant measures and for which one is able to describe a systematic
procedure to determine the basin of attraction of each invariant measure
(equilibrium state). ii) We use an explicit change of coordinates to prove that
every UFG diffusion can be, at least locally, represented as a system
consisting of an SDE coupled with an ODE, where the ODE evolves independently
of the SDE part of the dynamics. iii) As a result, UFG diffusions are
inherently "less smooth" than hypoelliptic SDEs; more precisely, we prove that
UFG processes do not admit a density with respect to Lebesgue measure on the
entire space, but only on suitable time-evolving submanifolds, which we
describe. iv) We show that our results and techniques, which we devised for UFG
processes, can be applied to the study of the long-time behaviour of
non-autonomous hypoelliptic SDEs and therefore produce several results on this
latter class of processes as well. v) Because processes that satisfy the
(uniform) parabolic H\"ormander condition are UFG processes, our paper contains
a wealth of results about the long time behaviour of (uniformly) hypoelliptic
processes which are non-ergodic, in the sense that they exhibit multiple
invariant measures.Comment: 66 page
Shot hole of stone fruits
Shot hole of stone fruits caused by the fungus Clasterposporium carpel s philum occurs yearly and is more difficult to control than Leaf Curl. It is often particularly damaging on early almonds, peaches, plums and apricots which come into growth in late winter or early spring while the weather is still cold and wet
On small time asymptotics for rough differential equations driven by fractional Brownian motions
We survey existing results concerning the study in small times of the density
of the solution of a rough differential equation driven by fractional Brownian
motions. We also slightly improve existing results and discuss some possible
applications to mathematical finance.Comment: This is a survey paper, submitted to proceedings in the memory of
Peter Laurenc
Late or Irish blight of potatoes
Late or Irish Blight, caused by the fungus Phythophthora infestans, is the most destructive disease of potatoes in many countries. Fortunately it has proved to be uncommon in the main potato areas of Western Australia as suitable weather for its epidemic development seldom occurs for sufficiently long periods. The disease is encouraged by periods of warm muggy weather during the day, followed by relatively cool night temperatures
Plant disease - crown gall of fruit trees
Crown gall is a widespread bacterial disease which affects many different plants. It is most frequently noticed on fruit trees particularly pome and stone fruits, but it also attacks grapes, berry plants, and ornamentals, including roses
Brown rot and collar rot of citrus
Plant disease
Brown rot is a serious disease of citrus, which fortunately has proved to be readily controllable. It attacks both leaves and fruits causing partial or complete defoliation, and a rather characteristic fruit rot. The disease may also affect the bark of citrus trees in the basal trunk region resulting in collar rot, or as it is sometimes called, brown rot gummosis. This phase of the disease will be referred to later
Plant disease - cereal smut diseases and their control
The well-known smut diseases of wheat, oats and barley are caused by fungal parasites which produce masses of soot-like fungal seeds or spores in the plants they attack, and it is from this dark coloured spore material that the name smut is derived
Topical notes on seed pelleting
IT is evident from recent correspondence, that during the coming season, many farmers wish to test the method of inoculating and pelleting seeds developed by the Department of Agriculture for treating seeds of plants such as subterranean clover. They are anxious to know how the pelleted seed is prepared, the conditions under which it may prove advantageous, and details regarding availability and cost of materials
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