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1997

Kouritzin, Michael, Dawson, Donald

A general Hilbert-space-based stochastic averaging theory is brought forth herein for arbitrary-order parabolic equations with (possibly long range dependent) random coefficients. We use regularity conditions onView the MathML sourcewhich are slightly stronger than those required to prove...

2008

Kouritzin, Michael, Long, H.

In this paper, we give a direct derivation of the Duncan–Mortensen–Zakai filtering equation, without assuming right continuity of the signal, nor its filtration, and without the usual finite energy condition. As a consequence, the Fujisaki–Kallianpur–Kunita equation is also derived. Our results...

1997

Kouritzin, Michael

Herein, an averaging theory for the solutions to Cauchy initial value problems of arbitrary order,ε-dependent parabolic partial differential equations is developed. Indeed, by directly developing bounds between the derivatives of the fundamental solution to such an equation and derivatives of the...

2014

Kouritzin, Michael, Ren, Y.-X.

Let ℓ be Lebesgue measure and X=(Xt,t≥0;Pμ) be a supercritical, super-stable process corresponding to the operator −(−Δ)α/2u+βu−ηu2 on Rd with constants β,η>0 and α∈(0,2]. Put View the MathML source, which for each smallθ is an a.s. convergent complex-valued martingale with limit View the MathML...

2020-01-01

Stephanie J. Peacock, Martin Krkošek, Andrew W. Bateman, Mark A. Lewis

Parasite transmission between farmed and wild salmon affects the sustainability of salmon aquaculture in Pacific Canada. Understanding and managing parasites in aquaculture is challenged by spatial and temporal variation in transmission dynamics. We developed a mechanistic model that connects sea...

2014-01-01

Jonathan R. Potts, Karl Mokross, Mark A. Lewis

Collective phenomena, whereby agent –agent interactions determine spatial patterns, are ubiquitous in the animal kingdom. On the other hand, movement and space use are also greatly influenced by the interactions between animals and their environment. Despite both types of interaction...

2009-01-01

Bampfylde, Caroline J., Jerde, Christopher L., Lewis, Mark A.

We formalize the establishment process for a sexual, semelparous organism through the use of hierarchical probability modeling from parameters of survival, probability of being female, probability of being fertilized, and expected fecundity.We show how to calculate the expected per capita growth...

2013-01-01

Krkosek, Martin, Orr, Craig, Peacock, Stephanie J., Proboszcz, Stan, Lewis, Mark A.

The resilience of coastal social-ecological systems may depend on adaptive responses to aquaculture disease outbreaks that can threaten wild and farm fish. A nine-year study of parasitic sea lice (Lepeophtheirus salmonis) and pink salmon (Oncorhynchus gorbuscha) from Pacific Canada indicates that...

2014-01-01

Peacock, Stephanie J., Connors, Brendan M., Krkošek, Martin, Irvine, James R., Lewis, Mark A.

The impact of parasites on hosts is invariably negative when considered in isolation, but may be complex and unexpected in nature. For example, if parasites make hosts less desirable to predators then gains from reduced predation may offset direct costs of being parasitized. We explore these...

2013-01-01

Merrill, E., Lewis, Mark A., Pybus, M., Potapov, A., Coltman, D.

We develop a model for the spread of chronic wasting disease (CWD) in a mule deer (Odocoileus hemionus) population to assess possible mechanisms of disease transmission and parameterize it for the mule deer population in Alberta, Canada. We consider seven mechanisms of disease transmission...