Stochastic inclusions and set-valued stochastic equations driven by a two-parameter Wiener process

2018 ◽  
Vol 18 (06) ◽  
pp. 1850047 ◽  
Author(s):  
Mariusz Michta ◽  
Kamil Łukasz Świa̧tek
Keyword(s):  
Wiener Process ◽  
Stochastic Equation ◽  
Stochastic Equations ◽  
Continuous Selection ◽  
Attainable Sets ◽  
Multivalued Solution ◽  
Stochastic Differential Inclusions ◽  
Multivalued Solutions ◽  
Two Parameter ◽  
Selection Of

In the paper we study properties of solutions to stochastic differential inclusions and set-valued stochastic differential equations driven by a two-parameter Wiener process. We establish new connections between their solutions. We prove that attainable sets of solutions to such inclusions are subsets of values of multivalued solutions of associated set-valued stochastic equations. Next we show that every solution to stochastic inclusion is a continuous selection of a multivalued solution of an associated set-valued stochastic equation. Additionally we establish other properties of such solutions. The results obtained in the paper extends results dealing with this topic known both in deterministic and stochastic cases.

scholarly journals Continuous Selection of the Fastest Growing Species in the Chemostat

2008 ◽  
Vol 41 (2) ◽  
pp. 9707-9712 ◽  
Author(s):  
Pierre Masci ◽  
Olivier Bernard ◽  
Frédéric Grognard
Keyword(s):  
Continuous Selection ◽  
Selection Of

Sample selection of prognostics validation test based on multi-stage Wiener process

2018 ◽  
Vol 233 (4) ◽  
pp. 605-614
Author(s):  
Zhiao Zhao ◽  
Yong Zhang ◽  
Guanjun Liu ◽  
Jing Qiu
Keyword(s):  
Wiener Process ◽  
Process Model ◽  
Failure Modes ◽  
Early Stage ◽  
Sample Selection ◽  
Degradation Process ◽  
Time Interval ◽  
Degradation Data ◽  
Multi Stage ◽  
Selection Of

Sample allocation and selection technology is of great significance in the test plan design of prognostics validation. Considering the existing researches, the importance of prognostics samples of different moments is not considered in the degradation process of a single failure. Normally, prognostics samples are generated under the same time interval mechanism. However, a prognostics system may have low prognostics accuracy because of the small quantity of failure degradation and measurement randomness in the early stage of a failure degradation process. Historical degradation data onto equipment failure modes are collected, and the degradation process model based on the multi-stage Wiener process is established. Based on the multi-stage Wiener process model, we choose four parameters to describe different degradation stages in a degradation process. According to four parameters, the sample selection weight of each degradation stage is calculated and the weight of each degradation stage is used to select prognostics samples. Taking a bearing wear fault of a helicopter transmission device as an example, its degradation process is established and sample selection weights are calculated. According to the sample selection weight of each degradation process, we accomplish the prognostics sample selection of the bearing wear fault. The results show that the prognostics sample selection method proposed in this article has good applicability.

Some lower bounds for the distribution of the supremum of the Yeh-Wiener process over a rectangular region

1975 ◽  
Vol 12 (04) ◽  
pp. 824-830
Author(s):  
Arthur H. C. Chan
Keyword(s):  
Lower Bound ◽  
Gaussian Process ◽  
Wiener Process ◽  
Lower Bounds ◽  
Upper Bound ◽  
Exact Distribution ◽  
Rectangular Region ◽  
Process With Independent Increments ◽  
Independent Increments ◽  
Two Parameter

Let W (s, t), s, t ≧ 0, be the two-parameter Yeh–Wiener process defined on the first quadrant of the plane, that is, a Gaussian process with independent increments in both directions. In this paper, a lower bound for the distribution of the supremum of W (s, t) over a rectangular region [0, S]×[0, T], for S, T > 0, is given. An upper bound for the same was known earlier, while its exact distribution is still unknown.

Widespread herbicide resistance in pigweed species in Ontario carrot production is due to multiple photosystem II mutations

2020 ◽  
Vol 100 (1) ◽  
pp. 56-67 ◽  
Author(s):  
Gareth Davis ◽  
Jocelyne Letarte ◽  
Christopher M. Grainger ◽  
Istvan Rajcan ◽  
François J. Tardif
Keyword(s):  
Photosystem Ii ◽  
Weed Management ◽  
Continuous Selection ◽  
Amaranthus Retroflexus ◽  
Cross Resistance ◽  
Single Mutation ◽  
Weed Species ◽  
Double Mutation ◽  
First Report ◽  
Selection Of

The apparent efficacy of linuron to control pigweeds (Amaranthus spp.) has declined in Ontario, Canada, in past decades, possibly due to resistance. Samples were collected in multiple fields across Ontario with reported linuron failure. These were characterized at the whole-plant and molecular levels. Screening with linuron revealed resistance in six out of nine green pigweed (Amaranthus powellii Wats.) populations and 36 out of 38 populations of redroot pigweed (Amaranthus retroflexus L.). Sequencing of the psbA gene showed resistant plants had mutations conferring resistance to photosystem II (PSII) inhibitors. The most commonly seen mutation was coding for a Val219Ile substitution, while other populations had Ala251Val or Phe274Val. Two populations were documented with a double mutation at Val219Ile and Phe274Val. All substitutions endowed plants with low to moderate resistance to linuron, with various levels of cross resistance to other PSII inhibitors. The double mutants were characterized by higher levels of resistance to linuron and diuron compared with each single substitution. The widespread failure of linuron to control pigweed species in many carrot fields in Ontario is due to the selection of PSII mutants. This is the first report of double mutation in psbA in any weed species and the first report of Ala251Val and Phe273Val in pigweed species. The presence of a double mutation is probably the result of continuous selection of plants already resistant due to a single mutation. Our results illustrate the need for diversified weed management strategies in crops where herbicide options are limited.

scholarly journals Continuous Interpolation of Solution Sets of Lipschitzian Quantum Stochastic Differential Inclusions

2007 ◽  
Vol 2007 ◽  
pp. 1-12
Author(s):  
E. O. Ayoola ◽  
John O. Adeyeye
Keyword(s):  
Continuous Selection ◽  
Stochastic Differential Inclusions ◽  
The Matrix ◽  
Finite Set ◽  
The Difference ◽  
Continuous Interpolation ◽  
The Given ◽  
Complex Valued ◽  
Locally Convex ◽  
Stochastic Differential Inclusion

Given any finite set of trajectories of a Lipschitzian quantum stochastic differential inclusion (QSDI), there exists a continuous selection from the complex-valued multifunction associated with the solution set of the inclusion, interpolating the matrix elements of the given trajectories. Furthermore, the difference of any two of such solutions is bounded in the seminorm of the locally convex space of solutions.

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